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ELEMENTS OF ELECTRIC TRACTION 



ELEMENTS OF 



ELECTRIC TRACTION 



FOR MOTORMEN AND OTHERS 



BY 



L. W. GANT 



LECTURER IN THE ELECTRICAL ENGINEERING DEPARTMENT OF THE 
LEEDS INSTITUTE TECHNICAL SCHOOL 




D. VAN NOSTRAND COMPANY 

23 MURRAY AND 27 WARREN STREETS 

NEW YORK 

1907 



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PREFACE 

"Elements of Electric Traction" is based upon a short series 
of lectures and practical demonstrations which have been given by 
the Author during the last two years to a class of motormen and 
others at the Leeds Institute Technical School. 

During these lectures and the subsequent period the writer has 
had repeated inquiries for a suitable textbook, and while he has 
recommended from time to time books dealing with the Elements 
of Electrical Engineering, as well as Handbooks for Motormen, he 
has always found a need for a book dealing in a simple manner with 
the fundamental, mechanical, and electrical principles underlying 
electric traction. To fill this need this work has been written. 

The work is intended to serve as an introduction to the more 
advanced works on electric traction, and to supplement the informa- 
tion given in the various Handbooks for Motormen and others. 

To make the work more helpful to students of Electric Traction 
generally, a number of formulae have been inserted, and, to further 
illustrate the text, examples have been added to the more important 
chapters. 

Electric Traction is a branch of Electrical Engineering of rapidly 
increasing importance, and the Author trusts that this volume will 
help those intending to follow up this career by giving them a sound 
knowledge of the fundamental principles of their subject. 

Finally, the writer takes this opportunity of thanking the following 
firms for having kindly given him diagrams and particulars of their 
traction controllers and motors : The British Thomson-Houston Co., 
Ltd. ; Dick-Kerr & Co., Ltd. ; The British Westinghouse Electric 



vi PREFACE 

and Manufacturing Co., Ltd. ; also Kaworth's Traction Patents, Ltd., 
and The Johnson- Lundell Electric Traction Co., Ltd., for particulars 
of their regenerative systems ; and the Eomapac Tramway Construc- 
tion Co., Ltd., for particulars and details concerning their patent 
tramrail. The writer also desires to thank Professor W. W. 
Haldane Gee for having kindly advised on the matter at an early 
stage, and also for a number of suggestions. 

L. W. GANT. 



Leeds, 

December, 1906. 



CONTENTS 



CHAPTER I 

INTRODUCTION 



Distribution of Electrical Energy 
Car Equipment — Path of Current 
Lightning Arresters 
Earth Switches — Leakage Lamps 
Lighting of Car 



PAOB 

1 
3 
6 

7 
8 



CHAPTER n 

PRINCIPLES OF MAGNETISM 

Magnetic and Non-magnetic Materials — Characteristic Properties of Magnets . 9 

Earth's Magnetism ........... 10 

Polarity — Magnetic Force — Magnetic Field — Magnetic Induction ... 11 

Retentivity — Methods of Magnetizing ........ 12 

Hysteresis — Lines of Force .......... 13 

Electro-magnetism — Electro-magnetic Laduction — Magnetizing Force — Per- 
meability — Magnetic Flux — Magnetization Curves — Magnetic Saturation . 14 
Magnetic Screening ........... 19 



CHAPTER in 

PRINCIPLES OF ELECTRICITY 

Effects of a Current ........... 20 

Electric Generator — Pressure — Current — Resistance ..... 21 

Conductors and Non-conductors . . . . . . . . 22 

Insulating Materials — Measuring Instruments ...... 23 

Heating Effect — Magnetic Effect — Chemical Effect ..... 23 

Ohm's Law 25 

Practical Proof of Ohm's Law ......... 26 

Drop — E.M.F. and P.D. of a Dynamo ........ 29 

Drop in Rail Return — B.O.T. Requirements ....... 30 

Electrical Terms — Positive and Negative Poles — Series — Parallel — Shunt — Short 

— Open Circuit ........... 31 

Coupling up Batteries in Series and in Parallel ...... 32 

Resistances in Series and in Parallel ........ 34 

Cables — Contact Surfaces . . . . . . . , . .37 

Fuses — Automatic Cut-outs .......... 33 

Examples 39 



VUl 



CONTENTS 



CHAPTER IV 

PRINCIPLE OF THE DYNAMO 

FAQE 

Fundamental Principle .......... 43 

Essential Parts— Essential Feature — Electromotive Force .... 44 

Right-hand Bule ............ 45 

Simple Dynamo — Simple Alternator ........ 47 

Uniform Pressure ............ 49 

Dynamo Construction — Commutator— Field Magnets — Series Dynamo — Shunt 
Dynamo — Compound Dynamo — Separately Excited Dynamo — Armature 

Core — Conductors ........... 50 

Characteristic Properties of Shunt, Series, and Compound Dynamos . . 62 

Motive Power ............ 55 



CHAPTER V 

PRINCIPLE OF THE CONTINUOUS-CURRENT MOTOR 

Fundamental Principle ........... 56 

Essential Parts — Essential Feature — Magnetic Blow-out .... 57 

Driving Force ............ 58 

Left-hand Rule 59 

Back Electromotive Force — Motor Starting Switches— Interlocking of Tramway 

Controller Handles .......... 60 

Examples ............. 65 



CHAPTER VI 

POWER AND POWER MEASUREMENT 



Principle of Work — Conservation of Energy ..... 
Power or Rate of doing Work — Horse Power — Force, Energy, and Power 
Electrical Energy and Power — Relation between Electrical and Mechanical 
Units — B.O.T. Unit — Method of measuring Electrical Power — Efficiency 

B.H.P.— Measurement of B.H.P 

Test of a Series Motor ..... 
Torque — Measurement and Calculation of Torque 
Motor magnetically considered .... 
Examples . 



67 
69 

70 
73 
75 
76 
81 
82 



CHAPTER Vn 

MECHANICS OF TRACTION 



Motion — Speed 87 

Acceleration ............. 88 

Accelerating Force . . . . . . . . . . .90 

Friction — Frictional Force — Resistance to Traction ..... 92 

Gradients and Gravitational Force . ....... 95 



CONTENTS 



IX 



Horse-power, and Energy expended in Traction 

Kinetic Energy— Heat Energy- — Potential Energy— Draw-bar Pull 

Gearing ....... 

Belation between Torque and Draw-bar Pull . 
Adhesive Force — Wear of Bails — Romapac System 
Measurement of Draw-bar Pull 
Formulae ..... 

Varying Draw-bar Pull — Car on Level 
Car on Gradient .... 

Examples ..... 



PAGE 

98 
99 
100 
102 
104 
105 
106 
108 
110 
112 



CHAPTER VIII 

CHARACTERISTIC PROPERTIES OF CONTINUOUS-CURRENT 

MOTORS 



Classification of Motors — Shunt Motor— Series Motor 
Compound Motors — Cumulative Compound Motor 

Motor — Self-regulating Properties . 
Speed and Power Regulation ..... 
Load ......... 



Differential Compound 



Motor Analysis ....... 

Shunt Motor — Speed Variation — Torque Variation . 
Series Motor — Speed and Torque Variation 
Particulars of Test of Traction Motor 
Speed Regulation — Varying Field — Varying Pressure 
Compound Characteristics — Motor Losses 
Secondary Actions ...... 



118 

119 
121 
123 
124 
125 
127 
131 
131 
138 
141 



CHAPTER IX 



APPLICATION OF MOTORS TO TRACTION 



Draw-bar Pull ....... 

Type of Motor — Series Motors as applied to Traction 
Series Parallel Control .... 

Controllers — Motor Cut-outs 

Controller Operations .... 

Putting into Series — Putting into Parallel 
Running on Series — Late Paralleling 
Regenerative Systems .... 

Raworth's Regenerative System 
Johnson-Lundell Regenerative System . 



143 
145 
151 
154 
157 
168 
160 
162 
165 
168 



CHAPTER X 



BRAKES 

General Principle ....... 

Kinetic Energy — Formulae . . . . . 

Classification of Brakes — Mechanical and Electrical 



171 
173 
176 



CONTENTS 



Board of Trade Regulations— Mechanical Brakes — Wheel-brakea 

Track-brakes ..... 

Electrical Brakes ..... 

Rheostatic Brake .... 

B.T.H. Magnetic Slipper-brake 

Westinghouse Magnetic Brake 

Application of Rheostatic or Magnetic Slipper-brake 

Emergency Brake — Application of Emergency Brake 

Regenerative Braking .... 

Brake Combinations .... 

Reversal of Motors .... 

Responsive and Non-responsive Actions . 

Examples ...... 



PAGE 

177 
179 
180 
183 
185 
187 
188 
189 
190 
191 
192 
193 
200 



ELEMENTS OF ELECTRIC TRACTION 

CHAPTEE I 
INTRODUCTION 

The following elements of electric traction are primarily intended to 
deal with the principles underlying the application of electrical 
power to traction, and more definitely with the electrical power as 
delivered to the trolley in an ordinary overhead system. In order 
that an idea may be formed as to the working of an electric traction > 
system as a whole, two diagrams are given, one of which illustrates 
diagrammatically the method of distributing such power, and the other 
illustrates also diagrammatically the parts of a car which are essential 
for the safe and effective utilization of the power. 

If the student does not understand all the terms used at the first 
reading of this chapter, he is advised to repeat the reading of it as he 
gets familiar with the later chapters. 

The source of energy employed in this country is the heat energy 
derived from coal, the coal being utilized for the generation of steam, 
engines being employed for driving large continuous-current multi- 
polar dynamos or generators, giving the requisite electrical pressure. 
This pressure, according to Board of Trade rules, must not exceed 
550 volts, as delivered to the trolley wire. 

Distribution. — The electrical power so generated is first delivered 
to the main switchboard for distribution, regulation, etc. On the 
main switchboard will be found all the main switches, fuses, circuit 
breakers, instruments, etc., for the controlling and operating of the 
various dynamo and feeder circuits, thus each dynamo and feeder 
circuit is controlled and safeguarded. Each dynamo has its own 
main switches, automatic circuit breaker, shunt regulator, etc., with 
the necessary instruments such as voltmeter and ammeter for in- 
dicating the pressure and current. By means of these switches the 
various dynamos can be coupled up in parallel so as to feed the 
circuits, or be cut out as the case may require. 

The current from the machines is thus delivered to what are 

B 



2 ELEMENTS OF ELECTRIC TRACTION 

called the main bus bars ; these consist of heavy copper bars which 
carry the whole output to the various feeder panels, where it is taken 
off for the various districts. Each district, or portion of such, as the 




fH 



case may require, is fed by means of a feeder cable, each feeder being 
controlled by its own set of main switches, circuit breaker, fuses, 
ammeter, etc., fitted on the main switchboard. 



INTRODUCTION 3 

The feeder cables are led underground to the section feeder 
boxes, and from these the overhead trolley wire is fed, as indicated 
below. 

The trolley wire is divided up — Board of Trade rule — into 
sections not exceeding half a mile in length, each half-mile section of 
the trolley wire being insulated from one another by section insulators. 

The section feeder box on each route generally feeds one section 
of the trolley wire, and the various sections are suitably connected 
together by means of switches, fuses, connecting links, etc., placed in 
what are termed the feeder boxes. The overhead trolley wire, being 
so subdivided and so connected, is not liable to entire breakdown 
in the event of any accident to one section of the trolley wire, as 
that section can be cut out, and the other sections fed by suitably 
cross-connecting by means of the switches, etc., fitted in the feeder 
boxes. 

In connection with the main switchboard there will also be what 
is generally called the Board of Trade panel, containing the various 
recording voltmeters, ammeters, and other instruments required for 
the various Board of Trade tests and records. 

Fig. 1 diagrammatically illustrates the above arrangement, two 
dynamos, one feeder circuit, and four sections of the trolley wire, 
simply being shown. In this diagram the dynamos and switches, 
etc., are shown in diagrammatic fashion, thus showing the method 
of diagrammatically illustrating the various parts of an electric 
circuit. 

The current, after passing down the trolley and through the car, 
returns to the generating station through the rails, cables being led 
from the rails at various points back to the main negative bus bar, 
and in this way the current is provided with a path back to the 
generators, a complete circuit thus being provided. As the rails are 
earthed, that is, connected with earth and so having the same 
electrical pressure, such a system is said to have an earthed return. 

Car Equipment. — The essential parts of a car equipment can be 
classified as follows : — 

(1) The necessary switches, circuit breakers, fuses, controllers, 
rheostats, or resistance boxes, for regulating and controlling the 
electrical power supplied to the motors ; also 

(a) Some form of lightning arrester, for safeguarding the car 

from a lightning discharge. 

(b) In some cases an earth switch, whereby in an emergency 

the trolley wire can be safely and effectively earthed, as 
may be advisable in the event of a trolley wire breaking. 

(2) The necessary motors, complete with gear wheels, etc. 

(3) The necessary switches, fuses, lamps, etc., for the effective 
lighiing 9f the car. 



ELEMENTS OF ELECTRIC TRACTION 



(4) The necessary hand brakes, sand boxes, and gear, life-guard 
attachments, gongs, signalling bells, destination indicators, etc. 

Different engineers adopt slightly different arrangments in con- 




nection with the above switches, etc., that shown in Fig. 2 being one 
of many. As the different arrangements are, however, more a 



INTRODUCTION 5 

matter of detail, the diagram given will enable the general purpose 
and principle to be understood. Following the path of the current 
by means of the diagram, it will be seen that after being collected 
from the trolley wire by means of the trolley wheel, it then passes, 
by means of a cable connection from the trolley head, down the 
trolley pole and standard to a main motor switch fitted at one end 
of the car under the canopy, within reach of the motorman or 
conductor as the case may be. From there it passes to the other end 
of the car to an automatic circuit breaker, this being similarly 
situated to the main motor switch. From the automatic circuit 
breaker the current then passes through a fuse, this being placed 
outside the car at one end, and from there through the choking coil 
to the main trunk leads which run under the car seats. The 
choking coil is connected with the lightning-arrester portion of the 
circuit, the purpose of which will be explained later. The arrester 
and choking coil are also often fixed under the seats of the car. 

The main trunk leads consist of two bunches of cables running 
from one end of the car to the other, and by means of these the 
controllers, motors, and rheostats are all connected ; the various 
cables being connected as they pass from controller to controller to 
the various armatures, fields, and rheostats. 

The particular path the current will take will depend upon the 
particular positions of the main and reverse drums of the controller 
in use. Assuming the power handle is on the first notch in series, and 
the reverse drum is in the forward position, the current will pass, not 
directly as here indicated, but by means of the various fingers and 
cables through the following path, the particular path indicated 
being that taken in a B18 (B.T.H.) controller. After leaving the 
choking coil the current will pass through the blow-out coil of the 
controller in use to the main trolley finger, and from there will pass 
by means of the various fingers and cables to K2 terminal on the 
resistance frame. The remainder of the connections then being such 
that E7 is connected to Al, AAl to Fl, El to A2, AA2 to F2, and 
E2 to earth wire, and so to frame, wheels, and rails. The current in 
this way, after leaving the choking coil, passes through the blow-out 
coil of one controller, and after passing through a certain amount of 
regulating resistance E2 to R7, it then passes through the armature 
Al to AAl and field Fl to El of No. 1 motor, and then through the 
armature A2 to AA2 and field F2 to E2 of No. 2 motor, and from 
there to earth wire, and so to wheels and rails, in this way finally 
completing its circuit back to the generating station. 

In some cases two circuit breakers are employed instead of one 
and a main switch, and sometimes the two circuit breakers are 
arranged in parallel; in this case, only one is employed at a time, 
the rear platform one being thrown off. 



6 ELEMENTS OF ELECTRIC TRACTION 

In other cases the fuse is dispensed with, the circuit in such 
instances being simply protected by means of the circuit breaker. 
The characteristic difference between these two methods of protecting 
a circuit will be dealt with later on. Where both are employed a 
double safeguard is obtained. 

Lightning Arresters. — A lightning arrester has two main 
functions to fulfil — one of providing a suitable path for the light- 
ning discharge, and the other of preventing current flowing from the 
trolley through that same path direct to earth. This is often carried 
out as follows : — 

Two metal or carbon contacts are provided, one of which is con- 
nected to the trolley cable and the other to the w^heels and so to rails, 
namely earth ; these two contacts, however, do not quite touch, a 
small distance separating them ; there is thus a small air gap breaking 
the circuit. In consequence of this no current will flow, the pressure 
of 500 volts being insufficient to break down the resistance of the air 
gap. Very often the air gap is so arranged in traction work that at 
least a pressure of 2000 volts would be required to break down, or, in 
other words, to spark across the gap. While the trolley pressure is 
thus insufficient, the tremendous pressure obtained with a lightning 
discharge amounting to thousands of volts will be more than sufficient, 
and so the discharge when such takes place can bridge across the 
air gap, and so to earth, and in this way a path is provided. To 
prevent, however, the discharge also finding its way through a 
parallel path, namely, that of any portion of the motor circuit to 
earth — the discharge piercing the insulation — a choking coil is 
inserted, as shown in the motor circuit. This may consist of a few 
turns of insulated wire wound in the form of a spiral or solenoid on 
to a wooden core. The action of this, as well as other portions here 
mentioned, will be better understood after reading through the 
principles explained in the following chapters. 

A lightning discharge is of an oscillating nature, somewhat 
similar to an alternating current, and the effect of such a current 
passing through a coil is to set up within the core a magnetic field, 
first in one direction, then in the other. The changing magnetic 
field, cutting across the turns of wire in the coil, sets up a back 
electromotive force similar to that obtained in a motor. The result 
is that of the two paths provided, the high-resistance one, due to the 
air gap in the lightning arrester, offers less total resistance to the 
discharge than that of the choking coil, which, as its name implies, 
tends to choke down any alternating current or discharge that tends 
to pass through it. In this way not only is a path provided for the 
lightning discharge in the arrester, but the motor circuit is also 
protected by means of the choking coil. 

When once the resistance of the air gap has been broken down 



INTRODUCTION 7 

by the discharge — the arc formed across the gap consisting of metal 
or carbon vapour having far less resistance than the air — a small 
pressure, comparatively speaking, will be able to maintain the arc. 
The result of this would be that after a discharge had taken place 
the trolley pressure would maintain the arc once formed, and in this 
way a dead short to earth would take place. The second function of 
the lightning arrester is to prevent this. This is often carried out 
electromagnetically : the electromagnet, being excited by means of 
the current flowing from the trolley, operates either a magnetic blow- 
out, or mechanically separates the two contacts. In this way the 
arc which is being maintained is ruptured, current ceases to flow, 
and the electromagnetic portion of the apparatus then ceases to act. 
If the contacts have been separated they will then return to their 
original position, and the operations will be repeated when the next 
discharge takes place. 

One method of carrying this out is shown in the diagram. A high 
non-inductive resistance — no back electromotive force is set up in 
a non-inductive resistance — is inserted in series with the air gap, 
and a portion of it is placed in parallel with the coil for operating the 
electromagnet. The lightning discharge takes the path through the 
non-inductive resistance to earth in preference to that through the coil, 
as this would have a choking effect. The current from the trolley, 
however, when such passes, being continuous in direction, prefers the 
path of least resistance to a continuous current, namely, that through 
the coil of the electromagnet. In this way, as soon as current begins 
to flow from the trolley through the arrester, the electromagnet 
automatically operates so as to break the circuit and prevent current 
from the trolley passing through the arrester to earth. 

Earth Switch. — An emergency-switching arrangement is some- 
times fitted to cars, so that in the event of a broken trolley wire the 
motorman can connect the trolley wire — the portion that is not 
down — direct to earth ; this causes a dead short which will blow 
the circuit breaker out at the power station, thus removing a source 
of danger from the streets, namely, a live trolley wire. This switch 
is entirely an emergency one, and is operated by the motorman 
breaking a glass, the breaking of the glass releasing a catch which 
holds the earth switch in its off position. 

Leak on Trolley Standard. — As a danger exists of the 
passengers getting a shock from the trolley standard in the event 
of the insulation of the cable or trolley lead breaking down, the 
trolley standard in this way becoming alive, the following method 
of detection for such is sometimes adopted : — 

Two lamps (tinted red) are coupled in series, one terminal is 
connected to the iron standard, and the other remaining terminal to 
earth. In the event of the insulation breaking down and the standard 



8 ELEMENTS OF ELECTRIC TRACTION 

becoming " alive," the lamps light up, and warning is thus given of 
the state of affairs, and the conductor can then warn passengers to 
leave the top of the car. 

Lighting. — One advantage of electric traction is that the car can 
be lighted electrically, and so much more effectively. For this 
purpose incandescent lamps are employed, these generally being 
100-volt lamps, and arranged five in series. With 500-volts pressure 
this means that each lamp has 100 volts across its terminals. The 
lighting cables are attached to the trolley side of the main motor 
switch, and in this way, by switching on the lights, the motorman 
can test whether the section is " alive " or " dead ; " that is, whether 
pressure is available for use or not. Each set of live lamps will be 
protected by a fuse and controlled by a suitable switch, the complete 
circuit also being protected by a main fuse. The lighting generally 
consists of interior lights, fore and aft signal, destination, dash, 
canopy, and roof lights. 

In an ordinary double-decker without roof these may amount to 
some seventeen lights, fifteen being in use at one time, one canopy and 
one dash-light only being lit at a time. This means three circuits, 
each circuit being composed of five lamps in series, one circuit being 
so arranged by means of switches that one canopy and one dash-light 
are always cut out. 

There are various arrangements of switches and lights adopted ; 
the one mentioned above will, however, indicate the general lines 
upon which these may be arranged. 



CHAPTER II 
PRINCIPLES OF MAGNETISM 

It has been found by experiment that only certain materials can be 
magnetized to an extent suitable for practical engineering purposes, 
and materials so magnetized are found to possess certain characteristic 
properties quite distinct and apart from any other properties they 
may possess. 

The word '' magnet " is supposed to have been derived from the 
place Magnesia, where it is supposed iron ores possessing similar 
properties were first discovered. 

The materials which can be magnetized are iron and steel and 
their alloys, though there are, it should be said, other materials which 
can be magnetized, such as nickel and cobalt, but these only to a 
very slight extent. 

The other materials in use in engineering work, such as copper, 
brass, gun-metal, zinc, and lead, can be treated as practically non- 
magnetic or non-magnetizable. It should, however, be added that 
certain alloys of iron can be made, such as a special mixture of 
manganese steel, which are only magnetizable to a very slight extent. 

At the outset it must be said there is nothing of an outward 
indication to show whether a body is magnetized or not, but if a 
straight bar of iron or steel be taken and magnetized in some way, 
that is, if an ordinary simple bar magnet be taken, it will be found 
on experimenting to possess the following magnetic properties : — 

That one end of the bar magnet will repel one end of another 
bar magnet, and attract the opposite end of the same magnet. Thus 
there is a mutual action either of attraction or repulsion set up 
between two magnetized bars, and depending upon this the follow- 
ing properties will also be found to exist on further experimenting — 

(a) That of setting or tending to set always in a certain direction, 
if carefully and delicately suspended, so as to be free to twist in any 
given direction. 

(b) That of attracting unmagnetized pieces of iron or steel, namely, 
magnetizable bodies ; strictly speaking, this is not quite true, as will 



lo ELEMENTS OF ELECTRIC TRACTION 

be seen later, the unmagnetized pieces of iron or steel really becoming 
^magnetized by induction, so the real action is between two magnets, 
as stated above. 

These fundamental experiments will now be dealt with a little 
more in detail, and from these will be obtained some knowledge of 
the characteristic properties of magnets generally. 

If a simple bar magnet be dipped into a mass of iron or steel 
filings, it will be found that the filings are attracted and cling to the 
magnet chiefly in two clusters, the clusters being at opposite ends, 
thus giving a rough indication that the magnetism is chiefly con- 
centrated in two places, or poles, as they are called, one being called 
the north, and one the south pole, the reason for which will be seen 
later. 

If a piece of copper had been dipped into copper or brass filings, 
no such action would have taken place, and if an unmagnetized bar 
of iron or steel had been dipped into unmagnetized iron or steel 
filings, again no such action would have taken place; also if a 
magnetized bar of iron or steel had been dipped into copper or brass 
filings, no attraction whatever of the filings would have occurred. 
The action only takes place between any material that has been 
magnetized and materials which can be magnetized. This principle 
is employed in the magnetic separation of iron and brass filings ; it 
also explains the reason copper oil-cans are often employed in con- 
nection with dynamos, as the ordinary tinned iron might be attracted, 
and so damage some portion of the machine. 

The reason for calling one end of the magnet a north pole and 
the other a south, is because, if a magnet be suspended as indicated 
above, it will be found to always set in one direction, namely, 
approximately due north and south ; that is, the end which is called 
the north pole is the end that always tends to point towards the 
north pole of the earth. If now a simple bar magnet be suspended, 
it will set as indicated approximately due north and south. On 
bringing near to the north end the corresponding end of another 
magnet, it will be found that the north pole of the one repels the 
north pole of the other, and that the north pole of the one attracts 
the south pole of the other, this being one of the fundamental facts 
in magnetism that like poles repel, and unlike attract. Thus there 
is a force of attraction between a north and a south pole, but a force 
of repulsion between two north poles or two south poles. 

Earth's Magnetism. — It has been found that the earth itself is 
a magnet possessing a magetic north and south pole, and it may just 
be mentioned that the magnetic north pole is not the geographical 
north pole, consequently in navigation an allowance has to be made 
for this fact. 

It is the action of the earth's magnetism acting upon the 



PRINCIPLES OF MAGNETISM ii 

maguetized needle, or bar of iron, which causes it to twist, and so set 
in a given direction. As it often leads to confusion, it should be 
noted that if that magnetic pole of the earth which lies approximately 
toward the actual north pole is a magnetic north pole, then the pole 
of the compass needle which is attracted in that direction must, since 
opposite poles attract, be a magnetic south pole. This difficulty is 
got over by calling the end of the compass needle which points 
northward, the north-seeking end or pole, or simply the north pole 
or end. 

The action of the earth's magnetism upon a magnetic bar is 
simply that of twisting it in a certain direction ; it will not tend to 
move it bodily, as can be tested by floating a compass needle in a 
bath of water, the reason for this being that while one of the 
magnetic poles of the earth will attract one end of the compass 
needle, that same magnetic pole will also repel the other pole of the 
small magnet with practically the same force, the length of a small 
compass needle being exceedingly small compared with the distance 
of the earth's magnetic poles. 

Polarity. — The north and south poles of a magnet cannot be 
separated. If a simple bar magnet be broken in two it will be found 
that each half contains a north and a south pole ; therefore wherever 
there is a north pole in that same bar there must also be a south 
pole. Sometimes it is useful to imagine such a thing as a free north 
pole, that is, a magnet possessing only a north pole, but such a thing 
actually is an impossibility. It is possible, however, to have magne- 
tization without having poles ; thus, if an ordinary straight bar be 
taken and magnetized, and then bent into a circle so that the north 
and south poles touch one another, the effect of these two poles when 
close together will be to simply neutralize one another's action on 
any external piece of iron or steel, yet the iron ring will be in a state 
of magnetization. 

Magnetic Force. — The force with which a magnet attracts or 
repels another magnet or any piece of iron or steel is called the 
magnetic force. This force will depend not only on the degree of 
magnetization, but also upon the distance the two magnets, or the 
magnet and the piece of iron, are apart ; the nearer they are the 
much greater will the force of attraction or repulsion be. 

Magnetic Field. — The space all round a magnet pervaded by 
the magnetic force is called the magnetic field of that magnet. A 
magnetic field may be due either to a magnet or to a number of 
magnets, or some equivalent of a magnet in the shape of a coil of 
wire through which a current of electricity is flowing. 

Magnetic Induction. — This is one of the most important facts 
connected with magnetism, namely, that magnetism is induced in a 
bar of iron or steel, or any magnetizable material — such as the alloys 



12 ELEMENTS OF ELECTRIC TRACTION 

of iron or steel — when the bar is brought within a magnetic field, 
that is, brought near, for instance, to another magnet. The nearer 
the iron to the magnet, or, in other words, the stronger the magnetic 
field it is placed in, the greater the inductive effect, that is, the more 
strongly willi the iron become magnetized ; the further away, or the 
weaker the field, the less the inductive effect, 

A north pole of a magnet will induce south magnetism in that 
part of the iron nearest to it, the corresponding north pole being in 
the end furthest away, and vice versa. This explains why a magnet 
attracts apparently unmagnetized pieces of iron or steel, magnetism 
being induced in the iron or steel, attraction then taking place between 
opposite poles, induction preceding attraction. 

Retentivity. — If a piece of very soft wrought iron be taken and 
magnetized inductively by placing it in a very strong magnetic field, 
it will be found that when either it is removed from the magnetic 
field or the magnetizing force be removed, the piece of soft iron 
retains or keeps only a very little magnetism, and what it retains it 
will very readily lose. If, however, a piece of steel be taken and 
magnetized in a similar way, it will be found that the steel retains 
more magnetism. This property of retaining is described by the 
word " retentivity," the steel having a greater retentivity than the 
soft iion ; the harder the steel, as a rule, the greater the retentivity. 

Compass needles, small horseshoe or bar magnets, are permanent 
magnets ; that is, their magnetism is that which they retain, and 
depends upon the retentivity of the steel from which they are made. 
These magnets are, comparatively speaking, weak, and for engineering 
purposes, where strong magnets are required, this retaining power is 
not solely depended on ; but by employing strong magnetizing forces 
in the shape of electric currents circulating through coils of wire 
surrounding the iron, very much more powerful magnets can be 
obtained, or, in other words, electro-magnets. 

In all magnetic experiments, then, it must be remembered that 
the permanent magnetism of a compass needle, for instance, is not 
very strong, and if a powerful magnet be brought very near a small 
compass needle, the magnetism which will be induced in the compass 
needle may overpower the permanent or residual magnetism, and 
thus a north pole may seemingly attract a north, whereas the strong 
north pole has induced a south, and the attraction is really between 
the north pole and the induced south pole. 

Methods of Magnetizing. — A bar of iron or steel can be 
magnetized either by means of permanent magnets, by stroking the 
bar, for instance, always in one direction with one end of a permanent 
magnet for a number of times, or electrically, as will be seen later 
when dealing with electro-magnets ; or again by placing a bar of iron 
or steel in a strong magnetic field, and so inducing magnetism, a 



PRINCIPLES OF MAGNETISM 13 

certain amount of which will be retained when the magnetic force is 
removed. Tapping it while in such a field will facilitate the 
process. 

This brings us to the theory of magnetism. One theory is that 
every individual particle of a bar of iron or steel is a small magnet, 
and that when the iron is in an unmagnetized condition it is supposed 
that all these small particles are simply mixed up in such a manner 
that there is no combined action, and consequently apparently no 
magnetization. The act of magnetization is to cause all these small 
magnets to turn more or less in one direction, and thus the effect is 
that of a number of small magnets assisting one another. 

Hysteresis. — If a bar of iron or steel be rapidly magnetized, 
first in one direction and then in the other, so as to rapidly reverse 
its polarity, it will be found to get hot. This is due to two causes : 
one electrical, which will not be considered here, and one magnetic. 
The harder the steel, or the greater its retaining power, the greater 
will be the amount of heat developed in a given time. Owing to the 
retaining power of the iron or steel, the magnetism does not readily 
change with alteration either in amount or direction of magnetic 
force ; in fact, a small reversing force has to be applied in order to 
actually rob the iron of the magnetism it retains, that is, its residual 
magnetism. In this way energy has to be expended in forcing the 
iron to behave in the desired manner, and this energy appears in the 
form of heat. This lagging of the magnetic state is called hysteresis, 
and the loss in heat due to this cause is termed the hysteresis loss, 
being entirely due to the magnets not responding to the magnetic 
forces at work. The softer and more pure the iron, the more readily 
will it respond, and the less heat will be developed in a given time. 

Lines of Force. — If a piece of paper be placed over, say, a bar 
magnet, and fine iron filings be then sprinkled on the paper, it will 
be found, on gently tapping the paper, that each little filing, having 
become magnetized by induction, sets itself in a given direction, due 
to the magnetic forces at work upon it. The direction is that of the 
magnetic force at that point, due of course to both poles of the magnet. 
It must be clearly understood that the iron filings only indicate the 
direction of the magnetic force in the plane or surface of the paper, 
and that magnetic force is acting in a similar way all round the 
magnet. It will also be noticed that where the magnetic force is 
strongest, that is, near the poles, there the iron filings are very much 
more crowded together than where the field is weaker. In this way 
the magnetic field due to various combinations of magnetic poles can 
be plotted and so studied. This has led to a conventional way of 
speaking about magnetic force, which enables not only the strength 
of field at any particular place to be specified, but also enables one to 
picture the distribution of the magnetic force. The method is to 



14 ELEMENTS OF ELECTRIC TRACTION 

represent force by lines — lines of magnetic force, as they are called 
— the greater the force the greater the number of lines in any given 
area, just as is graphically represented by the iron filings, a given 
force being represented by a given number of lines. This method 
of expression, although imaginary, is useful from many points of 
view. From this it will be understood how a certain number of 
lines are supposed to issue from the north pole of a magnet of given 
strength, and, after completing some sort of a path, re-enter the south 
pole of that same magnet. The particular direction the force is 
supposed to act has also been agreed upon, namely, from north to 
south, or that direction in which a free north pole would travel. 

When it is said the density of the magnetic lines is very great, 
or that the lines are very crowded together, it is meant that the 
magnetic force at that place is very strong. Where the lines are not 
dense, that is, where they are not crowded together, the magnetic 
force is not so great. If it is desired to employ the full strength of 
a magnet, then the full number of lines must be utilized as far as 
possible ; that is, lines must not be allowed to leak away along other 
paths than that desired, and if by any means lines can be concen- 
trated at the point where full use can be made of them, then the full 
magnetic force can be employed. This, it may be said, is a principle 
employed in dynamo and motor design. 

Electro-magnetism. — Experiments show that if a straight wire 
is held over and in line with a compass needle at rest, that is, in the 
magnetic meridian, as it is called, on passing a current of electricity 
through the wire, the compass needle is deflected, just as though a 
magnet had been brought near ; in brief, it is found that a current 
of electricity will produce a magnetic field, thus showing a certain 
relationship to exist between magnetism and electricity. A certain 
position of the wire with regard to the needle and a certain direction 
of current will give a certain deflection of the needle. The following 
rule will show what relation these have to one another : — 

Rule, — Take the right hand and place the thumb at right angles 
to the fingers ; now place the hand on the wire, fingers pointing in 
the same direction that the current is flowing, palm of the hand 
being toward the compass needle, then the thumb will point in the 
direction in which the north pole of the needle tends to move. This 
rule, also, by noting the deflection of the needle, enables the direction 
in which the current is flowing in a circuit to be determined, and so 
enables the polarity, say, of a dynamo or battery to be also determined, 
namely, which the positive and which the negative terminal. For 
an illustration of this, see Fig. 3. In the left-hand diagram the wire 
is over the needle nearest the reader ; in the right-hand diagram the 
wire is under the needle furthest from the reader. In each case 
current is supposed to be flowing from A to B, and the arrows 



PRINCIPLES OF MAGNETISM 



15 



indicate the direction the magnetic needle will tend to move, due to 
the action of the current. 

If now an insulated wire be wound into the form of a simple 

B 





Fig. 3. 



spiral or coil (solenoid, as it is sometimes called), as shown in Fig. 4, 
on passing a current of electricity through the coil it will be found 
on experimenting to act similarly to a bar magnet, one end of the 




Fig. 4. 



coil having north polarity and the other south. If the right hand 
with thumb at right angles be placed on the coil, fingers pointing in 
the direction i of current, the thumb will indicate which is the north 
end of the coil. 



i6 ELEMENTS OF ELECTRIC TRACTION 

Adopting the method already mentioned, a certain number of 
imaginary lines will be issuing from the north end of the coil, and, 
after completing some sort of circuit, enter the south. If now a bar 
of iron or steel, or, as is generally said, an iron or steel core, as 
shown by the dotted lines, be inserted inside the coil, it will be found 
that the bar of iron has become magnetized, and if the magnetizing 
force is at all a reasonable one, a far greater number of lines will now 
be issuing from the end of the coil than before. 

It is found that by these means magnetism can be induced to a 
much greater extent than any magnetism the steel will retain of 
itself, and in this way powerful electro-magnets can be made. If the 
current be stopped, the magnetizing force will cease, and the bar will 
lose nearly the whole of its magnetism, retaining, however, just a 
little, as previously explained. 

The magnetizing force, it has been found, in any given case, depends 
upon not only the number of turns of wire in the coil, but also upon 
the amperes flowing through the coil, the magnetizing force being 
proportional to what are called the ampere turns. If the number 
expressing the number of turns be multiplied by the number ex- 
pressing the amperes, a number will be obtained expressing the 
ampere turns. Thus, if in a given case the current be doubled 
and the number of turns be increased to three times the previous 
number, there will be 3 X 2, namely, six times as many ampere turns 
as before, and consequently six times the magnetizing force. Six 
times the magnetizing force, it must, however, be clearly understood, 
does not necessarily mean six times the number of magnetic lines, 
or, in other words, that the magnetic field has been increased to six 
times its original value. All this will depend, as will be seen later, 
upon the degree of magnetization of the iron. 

Permeability. — Having given, then, a certain magnetizing force, 
experiments show that iron or steel offers, as it were, far less resistance 
to the passage of these lines, than, for instance, air does, and con- 
sequently a far greater number of lines will be got with an iron core 
than with no core. This is expressed by saying the iron or steel is 
more permeable or has a greater permeability than air. 

If the number of lines obtained with, say, a certain specimen of 
wrought iron in the core be divided by the number obtained without 
the iron, a number will be obtained which will express the value of 
the permeability of this particular material with the particular 
magnetizing force employed. 

Example. — A long spiral of insulated wire is wound having 
fifteen turns of wire for each inch length of coil, 3 amps, are sent 
through the coil, thus giving 45 ampere turns per inch length of coil. 
With this particular magnetizing force, roughly speaking, there will 
pass through every square inch cross-section of the coil 150 lines, 



PRINCIPLES OF MAGNETISM 17 

that is, there will be a density of 150 lines per square inch ; this is 
generally expressed by saying there is a flux density of 150 lines. 
The total number of lines, or total flux, would be got by multiplying 
150 by the number of square inches cross-section in the core. 

A soft wrought-iron core is now made just to fit the inside of the 
coil, and is placed within it ; with this particular magnetizing force it 
will probably be found that 93,000 ]ines per square inch now pass 
through the core, therefore 93,000 divided by 150, namely 620, is the 
number expressing the permeability of this particular specimen of 
wrought iron with a magnetizing force due to 45 ampere turns per 
inch length of material. 

The more permeable, then, a material the more lines will be 
obtained, or, in other words, the stronger the magnets will be, with a 
given magnetizing force. The permeability of iron or steel is, how- 
ever, not a constant quantity, the permeability depending not only 
on the material, but also on the magnetizing force. There is a period 
reached, for instance, when any increase in the magnetizing force will 
not bring about any appreciable increase in the number of lines, the 
iron or steel having reached practically a state of magnetic saturation. 
Beyond this stage it would not be advisable to attempt to increase 
the magnetization, the return in the shape of increased lines of 
magnetization not warranting the expenditure in the shape of 
magnetizing force. Eoughly speaking, for ordinary soft wrought 
iron this state of practical saturation would be reached when there 
was a density of 100,000 to 120,000 lines or so per square inch. 
Higher densities than this can be obtained, but, as explained, it might 
be very inadvisable in practice to spend the energy in order to obtain 
such a density. Special makes of mild cast steel, it may be said, are 
now largely used in dynamo and motor construction. This steel will 
not give such good results as wrought iron for the lower densities, 
but gives equally good if not better for the higher densities, and is 
besides cheaper. 

As copper, brass, lead, and zinc are practically non-magnetic, the 
number of lines passing through a coil will be in no way altered, if a 
brass or copper core be inserted, from that originally obtained without 
anything in the core. The permeability of air, copper, brass, etc., is 
a constant quantity, and a little consideration of the above will show 
that in consequence of this, the ratio of the number of lines, say, 
with a copper core to the number of lines without the copper, is 
equal to 1 ; that is, the permeability of air, copper, brass, lead, and 
zinc has the numerical value 1. 

In Fig. 5 three curves are drawn — A for a specimen of cast iron, 
B for a specimen of cast steel, and C for a specimen of soft wrought 
iron. From this diagram it will be seen how the density of lines, or 
flux density, varies with the magnetizing force. The density of lines 

c 



i8 



ELEMENTS OF ELECTRIC TRACTION 



is given as the number of lines per square inch. The magnetizing 
force is given as the number of ampere turns for every inch length 
of path of the particular material. 

The magnetizing force required to send a given number of lines 
through a given magnetic path will depend not only on the total 
number of lines or flux, but upon the length, the area, and the per- 
meability of the material or materials forming the magnetic path ; 
thus, the longer the path, the more ampere turns will be required, the 
larger the area — that is, the less the density — the less ampere turns 



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will be required, also the more permeable the material, the less will 
be the number of ampere turns again required. 

The above curves are given to show that the flux density rapidly 
increases at first, and later on that a much larger magnetizing force 
is required to bring about an appreciable increase in the density ; the 
magnets approaching more or less a state of saturation. 

The magnetic circuit of a motor or dynamo is somewhat com- 
plicated, consisting as it does of various materials of various sections 
and permeabilities. Where the fields are not highly saturated, the 
greater part of the magnetizing force will be required to force the 
requisite flux across the air gap between the field magnets and 
armature, this being due to the very low permeability of air 
(namely, 1) compared with that of the iron or steel employed. 

From the diagram it will also be seen that to send 50,000 
lines per square inch through the specimen of cast iron requires 
some 105 ampere turns or so for each 1-inch length of the cast- 
iron path, whereas the cast-steel specimen only requires some nine 



PRINCIPLES OF MAGNETISM 19 

ampere turns, and the soft wrought iron some five ampere turns, for 
each 1-inch length of path, thus showing the much greater per- 
meability of the specimens of cast steel and wrought iron than of 
the cast-iron specimen. 

Finally, it may be said there is no material which will magnetically 
insulate a magnet so as to prevent it acting on, say, a piece of iron or 
steel, or even another magnet. By surrounding, however, a magne- 
tizable body with a good magnetic conductor, such as soft wrought 
iron, the body can be screened from magnetic influences, the magnetic 
lines or the direction of the magnetic force being diverted, another 
and an easier path for the lines being provided by means of the iron 
screen. 

As a practical illustration, an ordinary watch on being brought 
near a dynamo will in all probability be stopped, owing to the electro- 
magnets acting on the steel portions of the watch. If the watch, 
however, is placed in a wrought-iron tube, it will be found to be 
unaffected. 



CHAPTER III 
PRINCIPLES OF ELECTRICITY 

One of the first difficulties met with in this study lies in the fact 
that electricity cannot be seen, thus there is nothing of an outward 
indication to show when, for instance, a trolley wire is " alive " or 
" dead." By " alive " is meant when it is connected to a source of 
electrical supply, and so capable of supplying electricity at a given 
pressure, and by " dead " is meant when it is entirely disconnected 
and in no way charged ; thus there is notliing of a visible nature to 
indicate when, say, a trolley wire is charged or not charged, when it 
is safe or unsafe to handle. But while electricity cannot be seen, 
there are certain effects which a current produces when flowing 
through a circuit which can fairly readily be detected, provided one 
has suitable apparatus or instruments. The main effects which can 
be produced when a current is m-ade to flow through a given circuit 
are three in number ; one is always certain to be present to a greater 
or less extent, the other two may or may not be present. 
The following are these three effects : — 

1. Heating Effect. 

2. Magnetic Effect. 

3. Chemical Effect. 

Later on these effects will be dealt with more in detail, but at this 
stage the conditions requisite for the flow of a current of electricity 
through a given circuit will first be considered. These conditions are 
two in number — 

1. There must be a complete circuit for the current to flow 
through, that is, there must be a suitable path not only from the 
source of supply, but also back to the source of supply ; thus the 
trolley wire acts as the conductor for the supply and the rails act as 
the chief conductor for the return in most tramway systems. 

2. There must be a difference of electrical pressure between the 
two ends of a circuit through which a current has to flow. This 
difference of pressure may be obtained either directly or indirectly 
from some source of supply, such as a battery or dynamo. 

The flow of electricity can be compared somewhat with that of 
■water, but it must be remembered that, while it resembles it in some 



PRINCIPLES OF ELECTRICITY 21 

respects, it does not resemble it in all, and so the comparison can 
only be used for the purpose of illustration. 

Electric Generator. — An electric generator or dynamo produces 
a difference of electrical pressure, or, as it is often termed, a difference 
of potential, this being often expressed as the P.D., meaning the 
potential difference. An electric generator may be compared with a 
pump pumping water simply from one level to another, the difference 
of level producing a difference of pressure. 

Pressure. — A difference of electrical pressure, or a difference of 
potential, may be compared with a difference of water level, and just as 
a difference of water level or pressure is required for water to flow, 
so a difference of electrical pressure or potential is required for a 
current of electricity to flow. In practical work electrical pressure 
is measured in volts. 

Current. — A current of electricity is not the quantity of 
electricity, but the quantity of electricity passing per second. Com- 
pare again, say, the gallons of water delivered by a pump disregarding 
time, and gallons of water delivered per or during one second. 

In most cases it is more useful to know the quantity of electricity 
passing per second. In practical work the quantity passing per 
second is measured in amperes, so many amperes passing through 
a circuit means that a certain quantity is passing per second. When 
the quantity of electricity is spoken of, the term coulomb is used. 

Example. — If 3 amps, flow for 4 seconds through a circuit, then 
(3 X 4), namely 12, couls. quantity of electricity will pass through 
the circuit during the 4 seconds ; that is, 3 couls. per second, namely, 
3 amps. The value of the amperes multiplied by the time in seconds 
gives the value of the quantity of electricity in coulombs which pass 
through the circuit during the time considered. 

While a drop in electrical pressure will take place in the different 
parts of a circuit, as will be explained later, no loss in current will 
take place ; that is, the amperes flowing from any source of supply are 
exactly equal to the amperes flowing back to that same source of supply. 

Resistance. — It has been found by experiment that some 
materials offer much more resistance to the passage of a current 
than others ; thus, a copper wire y\j inch diameter, 1000 yards long, 
has a resistance of about 7|- ohms. An iron wire ^q inch diameter, 
1000 yards long, has a resistance of about 45 to 52 ohms. In 
practical work the resistance is measured in ohms. The iron wire, 
as will be seen from the above figures, has a resistance six or seven 
times that of the copper, and the copper wire is said to conduct 
electricity six or seven times better than the iron ; this means that 
with the same electrical pressure in each case across the ends of 
the wire, six or seven times more electricity will pass per second 
through the copper than through the iron wire ; in other words, six 



22 ELEMENTS OF ELECTRIC TRACTION 

or seven times as many amperes throngli the copper wire as through 
the iron wire. It should be noted the sole difference between the 
above two wires is simply tliat of material.* 

Conductors and Non-Conductors. — All metals, comparatively 
speaking, are good conductors of electricity. Copper is one of the 
best ; iron, as seen, conducts roughly only about one-sixth or one- 
seventh as well ; in other words, it has a resistance six or seven 
times that of copper. 

In comparing the resistance of two wires, two wires of the same 
size and the same length must be compared, because the greater the 
diameter of a wire, or the larger its area, the less its resistance ; the 
longer the wire, the greater its resistance. Some special alloys have 
a resistance fifty times that of copper, but even these materials are 
good conductors when compared with materials which are called 
non-conductors. 

Materials which have a very high resistance, and in consequence 
conduct practically no electricity, are called non-conductors, or 
insulators. These can be used for insulating a conductor ; that is, 
by means of such, electricity can be prevented from flowing from 
a conductor through any other path than the one desired. For 
instance, the resistance of the insulation of small electric-light cables 
1 mile long may be as much as 2500 million ohms, or, in other 
words, the insulation has a resistance of 2500 megohms per mile, a 
megohm being one million ohms. 

A good many considerations will have to be taken into account 
in deciding the most suitable material to be employed for insulating 
purposes, such as mechanical strength, liability to perish, etc., etc. 
Thus, in the case of cables, the insulation must have not only a high 
specific resistance, as it is termed, but must also be suitable for the 
conditions under which it has to be placed, such as being damp, and 
in some cases fireproof, not liable to rot or perish, etc., etc. The 
insulating material is sometimes called the dielectric. 

Practically speaking, water as ordinarily obtained is a good con- 
ductor, hence it is found that materials such as cotton, paper, 
asbestos, etc., which have a tendency to absorb moisture, and which 
are good non-conductors, or insulators, when dry, become very poor 
non-conductors, or, in other words, very bad insulators v/hen damp, 
their conducting power having been greatly increased owing to this 
absorption of moisture. As water is a conductor, sand is often 
employed to put out electrical fires, dry sand being a non-conductor, 
and so not liable to shortcircuit any live contacts or damage 
insulating material. 

* The terms " volt," "ampere," " coulomb," and "ohm" — also the term "watt," 
which will be explained later — take their origin from the names of various English and 
Continental scientists. 



PRINCIPLES OF ELECTRICITY 23 

The earth as a whole is also a good conductor, the more damp of 
course any portion is, the better will that portion conduct. It must 
be remembered, however, that while current may, in consequence of 
this, leak along other paths than those provided, as, for instance, 
partly through the earth in the return of a tramway system, the 
outgoing amperes, as stated above, from the generator, or source of 
supply, are equal to the ingoing amperes returning to the generator, 
or source of supply. 

Finally, there is no material which possesses no resistance, and 
no material which does not conduct a slight amount, but with insu- 
lating materials this slight amount is so exceedingly small as to be 
practically of no consequence. 

Insulating Materials. — The following are a few of the materials 
commonly used : china, glass, certain oils, mica, ebonite, fibre, 
papier mache, rubber, gutta-percha, silk, dry paper, dry asbestos, 
dry wood, dry cotton, etc. 

In addition to these, there are a great many special insulating 
materials manufactured and put on the market, which are used in 
practical work, these having special trade-names, such as : Ambroin, 
Uralite, Aetna Insulation, Psychiloid, Litholite, etc. 

Measuring Instruments. — The voltmeter is an instrument for 
measuring the volts pressure, more correctly speaking, the difference 
in pressure. This instrument must be connected across those termi- 
nals where there is a difference of pressure, and which difference 
requires measuring. 

The ammeter is an instrument for measuring the amperes, and 
has to be connected in series with the particular circuit through 
which one requires to know what current is flowing. 

There are instruments known as ohmmeters made for measuring 
resistance, but as a rule special methods are adopted for this purpose, 
on account of the great difference in value of the various resistances 
to be measured. For instance, a method suitable for measuring the 
insulation resistance of a cable, which may amount to a few million 
ohms, is not suitable for measuring the resistance, say, of an armature 
which may only be a fractional part of an ohm. 

Having now considered the two essential conditions for the flow 
of a current of electricity through a circuit, and having obtained some 
idea as to what is meant by electrical pressure, and what is meant by 
a current of electricity, also how various materials resist the passage 
of a current, the three main effects which may be produced when a 
current flows through a circuit will now be referred to — 

Heating Effect. — When a current is sent through a resistance, 
heat is developed, the greater the current or the greater the resist- 
ance, the greater the quantity of heat developed in a given time. 
Wherever there is resistance in an electrical circuit there heat will 



24 ELEMENTS OF ELECTRIC TRACTION 

be developed, to a greater or less extent, when current is passing 
through that resistance. 

The quantity of heat developed in a given time with a given 
resistance is proportional to the square of the current ; that is — 

If the current be doubled, 4 times the heat will be developed ; 

Three times the current, 9 times the heat will be developed ; 

One-half the current, one-quarter the heat will be developed ; and 
so on, the resistance being assumed to be constant. 

The quantity of heat developed, on the other hand, in a given 
time with a given current, is proportional to the resistance ; that is — 

If the resistance be doubled, twice the heat will be developed ; 

Three times the resistance, three times the heat will be developed ; 
and so on, the current in this case being assumed to be constant. 

The longer, however, a given current is allowed to flow through a 
given resistance, the greater will be the amount of heat developed ; 
that is — 

Twice the time, twice the amount of heat will be developed ; and 
so on, the current and resistance in this case being assumed 
to be constant. 

In all these cases one must distinguish between quantity of heat 
and temperature ; the temperature that any resistance attains depends 
not only upon the quantity of heat developed in a given time, but 
also upon the quantity of heat radiated or given out in the same time. 

When a state of balance is reached such that the quantity of 
heat given out in a given time is equal to the quantity of heat put 
in, then the body assumes a constant temperature. 

Example, — If 10 amps, were to pass through a resistance of 
10 ohms for 3 J minutes, an amount of heat would be developed 
which, if it were all utilized, would be sufficient to raise a pint of 
water from 60" Fahr. to 212° Fahr. — that is, just up to boiling-point. 

If 5 amps, passed through instead of 10, only one quarter the heat 
would be developed in the same time, or four times 3^ minutes, 
namely 14 minutes, would be required to raise the pint of water 
through the same number of degrees Fahrenheit. 

If, however, the resistance were 40 ohms instead of 10, and 5 
amps, passed through this resistance, then the same heat would be 
developed in 3^ minutes, as was the case when 10 amps, passed 
through the 10 ohms. 

Ordinary incandescent electric lamps are an example of the 
heating effect produced by a current, the carbonized filament in the 
lamp — which is exhausted of air, hence the noise when one is broken 
due to the inrush of air — simply becoming white-hot, and so incan- 
descent, when the full current passes through the lamp. 

Magnetic Effect. — The magnetic effects produced by a current 
have already been dealt with, and the reader is referred to Chapter II. 



PRINCIPLES OF ELECTRICITY 25 

Chemical Effect. — There are a great many chemical solutions 
through which, if a current is passed, decomposition of the liquid 
more or less takes place. This is called electrolysis, or an electro- 
lytic action is said to take place. For example, water is decomposed 
or split up into its constituent gases, viz. oxygen and hydrogen. 

In many of these cases the conductors where the current enters 
and leaves the solution are affected, a corroding or eating-away effect 
taking place depending upon the nature of the material, solution, etc. ; 
hence the bad effects of current leaking from the rails in tram- 
way-work, through the damp earth to pipes, and back again to 
rails. The Board of Trade rules are drawn up with the idea of 
reducing the resistance of the rail return, and so reducing the ten- 
dency for current to leak back other ways to the generating station. 

One or other of the above three main effects is generally employed 
in measuring instruments ; thus there are hot-wire ammeters and 
voltmeters which depend for their action upon the heating and the 
consequent expansion of a wire when a current passes through it. 
Similarly, there are electro-magnetic instruments which depend upon 
a magnetic action and the consequent attraction or repulsion of a 
coil when a current passes through the instrument. Again, there are 
certain classes of meters which depend upon a chemical action, these 
being called electrolytic meters. These are employed in measuring, 
either directly or indirectly, the power supplied to a circuit. 

Ohm's Law. — Experiments show that the current in a given 
circuit can be varied either by varying the pressure applied to the 
circuit, or by varying the resistance of the circuit. Ohm experi- 
mentally found the exact relation that exists between these three 
quantities, namely, pressure, current, and resistance, in any given 
circuit, and drew up a law, which is called Ohm's law. By means of 
this law or relation, if two out of the three quantities be known, the 
third can easily be calculated. The effects produced by varying 
(1) the pressure, (2) the resistance, will now be considered. 

(1) Variable Pressure. — If the resistance in any given circuit 
be kept constant, it will be found that increasing the pressure applied 
to the circuit increases the current, and decreasing the pressure 
decreases the current. Ohm found more exactly that in any given 
case, if the pressure applied to a circuit was increased to — 

Twice its value, the current was increased to twice its original 
value. 

Three times its value, the current was increased to three times its 
original value. 

Five and a half times its value, the current was increased to five 
and a half times its original value. 

One-half its value, the current was reduced to one-half its original 
value. 



26 ELEMENTS OF ELECTRIC TRACTION 

It may be mentioned here that the resistance of all pure metals 
increases slightly with rise of temperature. On the other hand, the 
resistance of some liquid solutions decreases with increase of tempera- 
ture. In the above the resistance is supposed, however, to have been 
kept constant. 

(2) Variable Resistance. — If the pressure applied to any given 
circuit be kept constant, it will be found that increasing the resist- 
ance decreases the current, and decreasing the resistance increases the 
current. Ohm found more exactly that in any given case, if the total 
resistance in the circuit was made — 

Twice as great, the current was reduced to one-half its original 
value. 

Three times as great, the current was reduced to one-third its 
original value. 

One-half as great, the current was increased to twice its original 
value. 

One quarter as great, the current was increased to four times its 
original value. 

Rough Practical Proof. — The following result of an actual 
rough test will approximately prove Ohm's law. Had the test been a 
more careful one. Ohm's law would have been proved more completely. 

A water resistance, consisting of a water-tight wooden box con- 
taining a weak solution of soda and water, and fitted with two 
movable lead plates, to which the cables were attached (see Fig. 6), 
was taken, and the following test was made : — 

(1) To show the actual effect of varying pressure. 

The plates in this experiment were not moved, so that the resist- 
ance was kept approximately constant. The pressure, however, was 
varied, and the following results were obtained. The pressure was 
that applied to the terminals of the water resistance, and was indi- 
cated by a voltmeter coupled as shown, the ammeter indicating the 
current that passed through the circuit — 

96 volts . . . 10| amps. 

48 „ . . . 5 „ 

24 „ ... 2L „ 

thus indicating that with half the pressure half the current, and with 
one quarter the pressure one quarter the current, or vice versa. 
The experiment was now varied — 

(2) To show the actual effect of varying resistance. 

A constant pressure of 24 volts was applied to the terminals of 
the water resistance. The plates in the first instance were 18 inches 
apart. In the second instance they were placed 9 inches apart, 
namely, half the original distance, the resistance in consequence 
being approximately halved. In the third instance they were placed 



PRINCIPLES OF ELECTRICITY 



27 



41 inches apart, the resistance then being approximately one quarter. 
The foUowinf? results were obtained : — 



Plates 18 inches apart 
9 

41 



2*37 amps. 
5 



thus indicating roughly that reducing the resistance to one-half its 
original value caused the current to increase to approximately twice 



BATTERY 




Fig. 6. 

its original value, and with one quarter the resistance the current 
was increased to approximately four times its value, or vice versa. 
It may now be stated that — 

1 volt pressure is required to drive 1 amp. through a resistance 
of 1 ohm ; therefore 

2 volts pressure will be required to drive 2 amps, through a 
resistance of 1 ohm ; 

3 volts pressure will be required to drive 3 amps, through a 
resistance of 1 ohm ; and so on ; 

and it also follows that — 

3 volts pressure will be required to drive 1 amp. through a 

resistance of 3 ohms. 
It has now been seen not only how the current varies with 



28 ELEMENTS OF ELECTRIC TRACTION 

varying pressure and resistance in a general way, but also how it 
varies in a more exact way, such that calculations can be made. 
Ohm's law is generally written thus — 

(1) ^ = 1'"" 

(2) CR = E ; or 

(3) R = ^ 

where E is equal to the number of volts pressure, 
E „ „ „ ohms resistance, 

C „ „ „ amperes. 

These are all short ways of expressing the same thing. Thus — 

(1) expresses the idea that if the number expressing the pressure 
in volts be divided by the number expressing the resistance in ohms, 
a number will be obtained expressing the value of the current in 
amperes that will flow through the given resistance with the given 
pressure across its terminals. 

(2) expresses the idea that if the number expressing the amperes 
be multiplied by the number expressing the resistance, a number 
will be obtained expressing the pressure in volts required to send 
the given current through that resistance. 

(3) expresses the idea that if the number expressing the volts 
across any part of a circuit be divided by the number expressing the 
amperes, a number will be obtained expressing the value of the 
resistance in ohms of that part of the circuit. 

Ohm's law can be applied to the whole or to a portion of a 
circuit ; the latter case, being the simpler and the more general, will 
be taken first. 

Examples. — (1) In a given circuit a pressure of 40 volts is being 
maintained across a resistance of 8 ohms : what current will be 
flowing through the resistance ? 

E 

Since C = :^, 40 -f- 8 = 5 ; that is, 5 amps, will be passing 

through the resistance. 

(2) Given that 40 volts pressure is required to send a current 
of 5 amps, through a resistance : what is the value of that resistance ? 

E 

Since R = -> 40 ~ 5 = 8 ; that is, the resistance will be 8 ohms. 

(3) What pressure will be required to send 5 amps, through 
a resistance of 8 ohms ? 

Since CR = E, 5 X 8 = 40 ; namely, 40 volts pressure will be 
required. 

The three examples given above are modifications of one and the 



PRINCIPLES OF ELECTRICITY 



29 



same case. In any one example two out of the three quantities are 
supposed to be known, the third being calculated. The last example 
indicates how the drop in pressure in any given resistance, or length 
of cable, for instance, can be calculated, the drop in pressure being 
defined as follows : — 

Drop. — The difference in pressure across any part of a circuit is 
the pressure required to drive whatever current is flowing through 



Vbt7M£TRP 

Ml 

4oyoit5' 

mm 



A,8ofiMS 



VOLTIACTtR. 





B.C>OHf^s 



M\ 

10 VOLTS. «- 

Maaaah 



/lMf»£R£<i. 



Fig. 7. 



that part, and that is the drop in pressure, sometimes simply termed 
the '' drop," which takes place in that part of the circuit. 

In Fig. 7 a dynamo is shown having 100 volts across its terminals. 
Three resistances, A, B, and C, of 8, 6, and 2 ohms respectively, are 
shown coupled up in series. These three resistances form the main 
or external circuit. Voltmeters are indicated, showing the pressure 
across various portions, and 5 amps, are supposed to be flowing 
through the circuit. 

In the resistance A there is a drop of 40 volts, or 40 volts are 
required to drive the 5 amps, through A. 

In the resistance B there is a drop of 30 volts, or 30 volts are 
required to drive the 5 amps, through B. 

In the resistance C there is a drop of 10 volts, or 10 volts are 
required to drive the 5 amps, through C. 

Forty added to 30 added to 10 makes 80, the remaining 20 volts 
(100 — 80 = 20) being required to drive the current of 6 amps, 
through the various connecting cables, etc., forming the remainder 

of the circuit, the resistances of these being, as E = — , 20 ~- 5, 

\j 

namely, 4 ohms. The dynamo will have to generate, as a matter of 



30 ELEMENTS OF ELECTRIC TRACTION 

fact, more than 100 volts, as a pressure will be required to drive the 
5 amps, through the dynamo itself. 

If the resistance of the dynamo — namely, the armature in a shunt 
machine — were 0*4 or 3% of an ohm, 2 volts would be required to 
drive the 5 amps, through the armature itself. Therefore the 
machine would have to generate, when 5 amps, were passing, a 
total pressure of 102 volts, a drop of 2 volts taking place in the 
armature, thus leaving 100 volts available for use. A voltmeter 
placed across the terminals of the machine, under these conditions, 
would indicate simply the pressure of 100 volts. Distinction has, in 
consequence of this, to be made between the full pressure a dynamo 
or battery may have, and the actual pressure available for use. The 
full pressure is sometimes termed the E.M.F. (electromotive force), 
while the pressure available for use is termed the P.D. (potential 
difference) at the terminals. The drop in pressure taking place 
depends not only upon the resistance, but also upon the current 
flowing, less pressure being available for use the greater the current. 
It must be noted, however, to prevent confusion, that the actual 
behaviour of any dynamo under varying load will depend upon the 
class of dynamo, as will be seen later ; and while some dynamos, 
owing to their self-regulating powers, increase their voltage, that is, 
the P.D. at the terminals, as the current increases, it must be clearly 
understood that in those instances the E.M.r. of the dynamo has 
been increased. In consequence, this in no way contradicts the 
statement that the greater the current the greater the drop in any 
given resistance, the P.D. always being less than the E.M.F. 

In the case of batteries, for instance, the E.M.F. can be obtained 
by putting a voltmeter across the terminals of the battery when the 
battery is on open circuit ; that is, when no current is flowing, the 
circuit being open or broken. It will now be understood that in 
applying Ohm's law to the whole of a circuit, not only must E equal 
the total pressure generated, that is, the E.M.F., but K must equal 
total resistance, including not only all instruments and connecting 
cables, but also the resistance of the dynamo or battery itself. In 
actual practice, however, in dealing with dynamo circuits, the various 
parts of the circuit are treated, as a rule, quite separately. In 
dealing with batteries, however, the circuit is very often treated as a 
whole. The resistance of instruments (ammeters) and cables can, in 
very many cases, be neglected, being small compared with the rest of 
the circuit. The resistance of the battery or dynamo is called the 
internal resistance, as compared with the external resistance, or the 
resistance in the external circuit. 

Drop in Rail Return. — The Board of Trade will not allow a 
greater drop than 7 volts to take place between any two points on 
the rails, in the case of tramway systems, where the rails act as a 



PRINCIPLES OF ELECTRICITY 31 

return conductor ; hence the reason for bonding, as every joint means 
so much electrical resistance, this being due to bad and indifferent 
contact, the copper bond across the joint providing a good conductor 
at the point where resistance is most likely to be introduced. 

It may also be mentioned here that the Board of Trade specify 
that the current density in the rails shall not exceed 9 amps, per 
square inch. As the cross-section of the average tramrail is about 
10 sq. ins. in area, the two rails will have an area of 20 sq. ins., and 
thus, according to Board of Trade rules, the maximum current 
returning down one pair of rails must not exceed 180 amps. The 
object of these rules is to reduce to a minimum electrolytic effects, 
as already mentioned. 

If the above limits are liable to be exceeded, means have to be 
adopted, in the way of return feeders and negative boosters, in order 
to keep the drop and current within the limits specified by the Board 
of Trade. 

Terms. — The following are a few of the terms employed in 
connection with the various methods of " coupling up " or connecting 
together electrical apparatus : — 

Positive rnd Negative Poles or Terminals — Series — Parallel — 
Shunt — Short — Open Circuit. 

Positive and Negative Poles or Terminals. — One terminal 
or pole of a battery or dynamo is termed the positive, generally 
written thus + ; the other the negative, written thus — . Current is 
said to flow from the positive pole or terminal of a battery or 
dynamo, through the external circuit, back to the negative pole or 
terminal of a battery or dynamo. Through the battery or dynamo, it 
will be noted that the current flows from the negative to the positive, 
but as in this connection the external circuit is always referred to, 
the current is said to flow from the positive to the negative terminal. 

Series. — Whenever two or more portions of a circuit, such as 
two or more dynamos, are said to be coupled up in series, it means 
that whatever current is flowing through the one, the same current 
will also be flowing through the other. Thus in Fig. 7 the resistances 
A, B, and C are all in series, the current that goes through A going 
through B and C. 

Parallel and Shunt. — If certain portions of the circuit are so 
coupled up that the current has a choice of paths, so that part can go 
one way and part another, then these paths through which the 
current can divide are said to be in parallel. Thus in Fig. 7 the 
current coming from the dynamo has a choice of paths, part will go 
through the external circuit, namely, the resistances A, B, and C, 
which are in series with one another, and part will go through the 
field- magnet winding. The field winding in this case is said to be in 
parallel with the external circuit. In this particular instance, however, 



32 ELEMENTS OF ELECTRIC TRACTION 

the field would only be taking a small fraction of the total current, 
in other words, a small fraction of the total current is being shunted 
through the field coils ; and in cases like this, the field is said to be 
coupled up as a shunt across the terminals of the dynamo. It may 
here be noted that a dynamo of this particular class is called a shunt 
dynamo. 

Short. — This term is employed to indicate that some path has 
been provided of practically no resistance, so to speak — some short 
cut for the current. This may apply to a portion of a circuit or to 
the whole of a circuit; thus, when the term *'dead short" is 
employed, it indicates that some path of practically no resistance has 
been provided across either the main terminals of the machines or 
the main terminals of the supply ; thus, to connect a trolley wire 
when alive direct with the rails would " dead short " the trolley wire. 
This, of course, is a procedure that no one would adopt unless special 
circumstances demanded it, as, for instance, when a trolley wire 
breaks and the " earth switch " is employed with the distinct object of 
earthing that " section," and '^o removing a serious source of danger. 
To dead-short a dynamo, or to dead-short a section of a trolley 
wire to earth, would cause an excessive current to flow, which, 
unless some safety device, such as a fuse or " cut-out," were in the 
circuit, would cause serious damage. The reason for this large 
current being simply due to the fact that whatever other paths there 
are, the " short " has provided one of practically no resistance, and 
by Ohm's law the less the resistance the greater the current. It is 
owing to these large currents, when a short occurs, that such 
excessive heat is developed, which brings about such destructive 
arcing, and the actual fusing or melting and burning of the metal 
forming the short, and the parts adjacent to it. It may be mentioned, 
however, that occasionally instruments or portions of a circuit are 
" shorted" with the object of protecting that particular portion ; thus, 
sometimes delicate galvanometers are shorted, in this case the large 
current that might be flowing flows through the " short," and does not 
flow through the galvanometer. In cases of this sort, however, the 
shorting of the portion chosen does not appreciably alter the value of 
the current, the resistance of the portion shorted being small com- 
pared with the resistance of the rest of the circuit. 

Open Circuit. — This term is employed to describe a circuit which 
is open or broken, that is, incomplete. Consequently, with an open 
circuit no current can flow. 

In Fig. 8 two batteries are shown coupled up in series, and in 
the external circuit four resistances are shown coupled up in parallel. 

In Fig. 9 two shunt-wound dynamos are shown coupled up in 
parallel. In the external circuit the resistances A and B are shown 
coupled up in series with one another, and in series with three 



PRINCIPLES OF ELECTRICITY 



33 



\ 



1 



resistances C, D, and E, the three resistances C, D, and E being, 
however, in parallel with one another. 

In connecting two dynamos or two batteries in series, it will be 
noticed that the positive pole of 
one battery or dynamo is coupled to 
the negative pole of the other. In 
this way each battery or dynamo 
is tending to drive current the same 
way, hence they assist one another. 
If, however, the positive pole of 
one be connected to the positive 
pole of the other, and the circuit 
be completed as shown in Fig. 10, 
then if the E.M.F. of the one bat- 
tery or dynamo were exactly equal 
to that of the other, as they are 
now opposing each other, no cur- 
rent would flow. If one had a 
greater E.M.F. than the other, then 
a current would flow — depending 
upon the difference in pressure — 
in that direction in which the one 
with the greater E.M.F. was tend- 
ing to send it. 

In coupling up dynamos or batteries in parallel, it will be noticed 

tWMA 



'-A/WWWVWWV^' 
"-AM/WWWWW^' 
^-AWWWVWWW^' 
'-AA/WWVWWWV' 



Fig. 8. 




Fig. 9. 



that all the positive terminals are coupled together, and all the 
negative, and that the external circuit is taken from the positive side 



D 



34 



ELEMENTS OF ELECTRIC TRACTION 



back to the negative side; thus the current through the external 
circuit will be the sum of the currents delivered by the various 
batteries or dynamos. 

Wherever dynamos or batteries are coupled in parallel, with the 
object of their supplying current to an external circuit, it is essential 
that their E.M.F.'s should be alike, otherwise the one with the greater 
E.M.F. will overpower the one with the less, forcing a current through 

the reverse direction ; the battery or dynamo with the lesser 



m 



rVAWM 
+ + 



rvA/WWWV 




I 



I 



Fig. 10. 



E.M.F. in this case absorbing electrical energy, and so not delivering 
any. 

It will now be noted that a voltmeter is an instrument which is 
always coupled up as a shunt, or in parallel with that portion of the 
circuit the voltage of which has to be measured, while the ammeter is 
an instrument coupled in series with the circuit, the current of which 
has to be measured ; consequently, in a general way a voltmeter 
possesses a considerably greater resistance than an ammeter. 

It may be mentioned here that there is a certain class of ammeter, 
in which the actual instrument is coupled as a shunt across the 
terminals of a special resistance, supplied with the instrument. In 
this case the instrument has only passing through it a certain fraction 
of the total current, but is so marked off to read as if the total current 
were going through it. This class of instrument is very suitable for 
use where large currents have to be measured. 

Resistances in Series and in Parallel. — It has been shown 
that if the total pressure which a battery or dynamo is capable of 
giving be divided by the total resistance in circuit, the value of the 
current is obtained. When resistances are in series, in order to get 
the total resistance, all that need be done is to add the various 
resistances together ; thus, in Fig. 7 the total resistance of the three 
resistances A, B, and C is equal to 16 ohms. 



PRINCIPLES OF ELECTRICITY 



35 



When, however, resistances are in parallel, it is not such a simple 
matter to calculate their joint resistance. 

To take a simple case : if a wire resistance, say of 5 ohms, be 
taken, and a pressure of 100 volts be applied to the terminals, 
20 amps, would pass through the resistance. If, now, anotlier 
similar resistance of 5 ohms be placed in parallel with the first, it 
will be seen that the area of the path has been increased, there being 
two wires now in place of the one, and the result in the total or joint 
resistance of the two is less than before ; in fact, the joint resistance 
is less than either of them singly. As a matter of fact, the joint 
resistance in the above case would be 2J ohms. 

To illustrate this the following test was made : — 

Rough Test. — Two water resistances were taken, and the 
following results were obtained on applying the pressure of 44 and 
30 volts respectively to the terminals of the two resistances : — 



No. 1 Water PtEsiSTANCE 



Volts. 


Amps. 

^2 


Res. 


44 


— = 17*6 ohms 



No. 2 Water Resistance 



Volts. 


Amps. 


Res. 


30 

■ 


2i 


, = 12 ohms 



Thus the resistance of No. 1 was found to be 17'6 ohms, and the 
resistance of No. 2 was found to be 12 ohms. 

The two resistances of 17 '6 and 12 ohms were then coupled in 
series, and a pressure, as can be seen, of 74 volts was rec|uired to send 
2J amps, through the two in series ; the pressure required being the 
sum of the two previous pressures, the combined resistance of the 
two in series being 29*6 ohms, as is proved by the experiment, 
74 -f- 2-5 being equal to 296. 

The resistances were then coupled in parallel, and on applying 
the pressure of 74 volts the following result was obtained : — 



36 



ELEMENTS OF ELECTRIC TRACTION 



Nos. 1 AND 2 Water Resistances in Parallel 



Volts. 


Amps. 


Combined Res. 


74 


Hi "^^^ - G-57 ohms 



The current of 11^ amps., it must be noted, is a much greater 
current than would be obtained with either of them singly with the 
pressure of 74 volts applied at the terminals ; as a matter of fact, the 
lesser resistance, namely No. 2, with this pressure would only have 
allowed some 6J amps, to pass through it. 

Thus the joint resistance of the two was found by rough 
experiment to be (dividing 74 by 11^) 6*57 ohms. 

Calculating the joint resistance from the figures 17'6 and 
12 ohms, a joint resistance of 7'1 ohms is obtained. 

Had the experiment been carried out more carefully, the calculated 
resistance would have been found to agree more accurately with the 
actual joint resistance measured. 

It should be pointed out that the current of 11| amps, would 
divide, part going through one resistance and part through the other ; 
the amount passing through each depending upon their relative 
conducting powers. 

The following is the method of calculating the joint resistance of 
a number of resistances in parallel : — 

Example — 

To calculate the joint resistance of three resistances of 2, 3, and 
4 ohms each, placed in parallel, proceed as follows — 

The resistance of 2 ohms will only conduct half the current that 
1 ohm would. 

The resistance of 3 ohms will only conduct one-third. 

The resistance of 4 ohms will only conduct one-fourth. 

Adding i -f ^ + i, we get, as — 



\ equals 



6^ 1 
12> 3 



equals j'^, and I equals ^2> ^ total of ||^ 



Thus the joint conductivity is }f that of 1 ohm. 

On the other hand, the resistance, that is, the combined resistance, 
is If of 1 ohm, namely, just under 1 ohm. 

Thus the joint resistance of 2, 3, and 4 ohms in parallel with one 
another is, roughly speaking, equivalent to a resistance of 1 ohm. 

The following are a few practical notes dealing with cables, con- 
tact surfaces, fuses, and automatic cut-outs : — - 



PRINCIPLES OF ELECTRICITY 37 

Cables. — There are two methods eraployed in specifying the size 
of cables — 

1. As cables are built up of a number of strands of wire, one 
method is to specify both the number of wires forming the strand of 
the cable, and also the gauge — thus a j-§ cable means that the cable is 
composed of nineteen wires of 16 gauge, the gauge taken being that 
of the standard wire gauge ; again, a -^-J cable would be a cable com- 
posed of thirty-seven strands, the gauge of each strand being No. 12. 

2. Another method of specifying large cables is sometimes 
adopted, namely, to simply specify the area in square inches of the 
conductor — thus a 0'4 cable means a cable which has an area of 0*4 
sq. inch, that is, 1% sq. inch ; this means that if the area of each 
small wire composing the strand be taken, and all the areas be 
added together, the total area of the conductor will be obtained, 
which in this case is j*q of 1 sq. inch. 

A common rule to determine the number of amperes which a 
cable or wire can carry is to multiply the number of square inches 
area of the cable by the number 1000. In other words, to allow 
1000 amps, for every square inch of area — thus a 0'4 cable would 
carry 0*4 x 1000, namely, 400 amps. Where cables are specified in 
the former manner, in order to obtain the area, the area of the cable 
must be calculated from the number of wires and their gauge. As a 
matter of fact, however, cable-makers generally publish tables giving 
this and other information concerning the cables they manufacture. 

The above rule is only a rough one, and, in some cases, cables 
would be run at nothing like 1000 amps, per square inch if of con- 
siderable length, as a considerable drop of pressure might be taking 
place in the cable, and this very often is a decided objection in 
itself, apart from the question of loss of energy. From a heating 
point of view, small cables can be run at higher densities than large 
ones, as small cables have more cooling surface in comparison with 
their size. The heating effect and "drop" are the two main con- 
siderations which have to be taken into account in determining the 
size of cable to be employed. 

A good rule to remember is that when cables are run at 1000 
amps, to the square inch, a drop of 2 J volts will take place in the 
cable itself for every 100 yards of actual length. 

It may be noted that the class of insulation for a cable, that is, 
the material of which it is composed, and its thickness, will depend 
upon the pressure that it will have to carry, and the use to which the 
cable is going to be put; the greater the pressure the better the 
insulation will have to be, that is, the insulation resistance will have 
to have a higher value. 

Contact Surfaces. — All contact surfaces for making electrical 
contact between any two parts should be not only of sufficient area, 



38 ELEMENTS OF ELECTRIC TRACTION 

but should be clean and make good contact. If they are of insufficient 
area, or dirty, or not making good contact, resistance is introduced, 
and heat in consequence is developed. 

The fingers on a controller barrel, or the brushes on a commutator, 
or the blades of a switch, are examples of contact surfaces. It 
depends upon the kind of contact as to what area it will have to be 
in order to carry a given current. In some form of switches specially 
designed for making good contact, as many as 300 amps, to the 
square inch can be allowed, the material in this case being copper. 
In other forms of contact possibly only some 50 amps, or so to the 
square inch would be advisable. 

Fuses. — With the object of protecting the various parts of a 
circuit in case an excessive current should flow, fuses are inserted in 
the circuit. These generally consist of a copper, lead, or tin — some- 
times a special alloy of the last two — wire, or strip of such a cross- 
sectional area as to melt and so burn out and break the circuit 
before damage can be done to the remainder of the circuit. Special 
means have to be adopted in breaking heavy currents to " blow out " 
the arc formed. 

Automatic Cut-outs. — Automatic cut-outs or circuit breakers 
such as the canopy cut-out fitted at one end of a tramcar are for the 
same purpose, and generally consist of a special form of switch which 
automatically operates, say, when an overload occurs. The auto- 
matic action is often brought about by means of an electro -magnet. 
Here, again, special means have to be adopted to prevent arcing. 

In comparing these two methods of safeguarding a circuit, it 
should be remembered that the danger to a circuit depends not only 
on the excessive current that may be flowing, but also upon the time 
it is allowed to flow, as the heat developed with a given resistance 
depends upon both time and current. The difference, then, between 
an ordinai'y excess current, automatic cut-out, and a fuse, lies in the 
fact that a fuse intended to blow, say, at 50 amps., may carry 75 
amps, if such an overload is only on for a few seconds, the heat 
developed, as already seen, depending upon the time. In this way 
the fuse resembles the rest of the circuit, such overloading for such a 
short time doing no damage, and the circuit is not needlessly broken ; 
in short, the damage done to the circuit depends upon the length of 
time the overload is carried, and the current the fuse will blow at 
will depend to a certain extent in a similar manner upon the length 
of time the current is flowing. 

An ordinary automatic cut-out, that is, one not fitted with some 
time element device, as it is generally termed, may, on the other hand, 
carry for any length of time a very heavy current, say just under 
what it will blow at, without operating ; time here not entering into 
the question at all. It, however, has the advantage that it is readily 
operated and easily replaced when once the circuit has been broken. 



PRINCIPLES OF ELECTRICITY 39 

Examples 

(1) A 100-volt 16-c.p. incandescent lamp when connected across a 
100- volt circuit takes 0*6 of an ampere. 

What is its resistance when so connected ? 

As R = 7i .*. R = TT-T = 166'6 ohms 
L U*b 

Therefore resistance of lamp when fully illuminated or resistance 
when hot = i66*6 ohms. 

It should be noted, as a matter of fact, that the resistance of the 
carbon filament when cold will be much greater than this, having 
possibly twice the above value. 

(2) A voltmeter reading up to 600 volts has a resistance of 
40,000 ohms. 

What current will pass through the instrument when it is 
registering 500 volts ? 

As 0=1 .-. C = -4-0^0 = ^, or 0-0125 amp. 

Therefore the current that will pass through the instrument when 
registering 500 volts = 0*0125 amp. or 12-5 milliamperes. 
A milliampere = yooo P^^^ ^^ ^^ ampere. 

(3) A rheostat or regulating resistance for starting a motor has a 
total resistance of 6^ ohms. 

(a) What drop in pressure will take place in the total resistance 
when a current of 60 amps, is flowing through it ? 

(b) What pressure will be available for driving current through 
the remainder of the circuit if 500 volts is the pressure of supply ? 

(a) . . . As E = CR .*. E = 60 X 6-5 = 390 volts 

Therefore drop in pressure taking place in the resistance when 
60 amps, are flowing = 390 volts. 

(6) Pressure of supply = 500 volts 

Drop of pressure in resistance = 390 volts 
.-. 500 - 390 = 110 volts 

Therefore pressure available for driving current through the 
remainder of the circuit =110 volts. 

(4) A Leclanche cell has an E.M.F. of 1*5 volts and an internal 
resistance of 1*5 ohms. 

What will be the P.D. across its terminals when sending current 
through a resistance also of 1'5 ohms ? 



40 ELEMENTS OF ELECTRIC TRACTION 

E.M.F. = 1-5 volts 
Total res. of circuit = res. of cell -f- res. in external circuit 
.*. total resistance of circuit = 1'5 + 1-5 = 3 ohms 

As C = :p .-. current = -^ = J amp. 

" Drop " of pressure in cell = CE = J x 1-5 = 0*75 volt 

.-. P.D. = 1-5 - 0-75 = 0-75 volt 

Therefore P.D. across terminals when |- amp. is flowing = 075 volt. 

(5) What would be the P.D. in the above example if the resist- 
ance of the external circuit was — 

(a) 13-5 ohms ? 
{h) 148-5 ohms ? 

W . . . AsC=^^i^. = J|=J,-amp. • 

" Drop " of pressure in cell = j^ X 1*5 = 0'15 volt 
.'. P.D. across terminals = 1"5 -- 0"15 = 1*35 volts 

Therefore P.D. across terminals when ji^ amp. is flowing 
= 1-35 volts. 

(6) . . .AsC=j,^-^^ = J|^=TJoamp. 

"Drop" of pressure in cell = yJ^f, x 1'5 = O'OIS volt 
.*. P.D. across terminals = 1'5 — 0*015 = 1-485 volts 

Therefore P.D. across terminals when ^Vo ^^P* is flowing 
= 1*485 volts. 

Note. — The less the current, the more nearly does the P.D. equal 
the E.M.F. 

(6) Ten Leclanche cells, each having an E.M.F. of 1*5 volts, and 
an internal resistance of 1'5 ohms, are coupled up in series, eight 
assisting one another, and two assisting one another but opposing the 
eight. A resistance of 3 ohms is placed in the external circuit. 

{a) What current will flow through the circuit ? 

{Ij) What will be the P.D. across the terminals of the 10 cells ? 

(a) . E.M.F. due to the 8 cells = 8 x 1-5 = 12 volts 
E.M.F. due to the 2 cells = 2x1-5=3 volts 
Effective E.M.F. for driving) __ ^^ q _ n u 
current through the circuit 5 - J-^ - '^ - «^ volts 

Note. — The 3 volts are acting in opposition or as a back E.M.F. 



PRINCIPLES OF ELECTRICITY 41 

Internal resistance of the 10 cells =^ 1*5 X 10 = 15 ohms 
Kesistance of external circuit = 3 ohms 
.*. total resistance in circuit = 15 + 3 = 18 ohms 

As C = g /. C = f^ = i amp. 

Therefore current flowing through the circuit = ^ or 0-5 of an 
ampere. 

(b) .... Eesistance of the 10 cells = 15 ohms 
As E = CR, .*. drop taking place in ) ^ ^ , 
the 10 cells = 1 X 15 ^ = V-5 volts 

Effective E.M.F. across the ) __ ^ , 
terminals of the 10 cells f ^ ^ ^^^^^ 

.*. P.D. across the terminals ) ^ - ,, 
of the 10 cells = 9 - 7-5 f = ^'^ ^^^^^ 

Therefore the P.D. across the terminals of the 10 cells when 
^ amp. is flowing = i*5 volts. 

Note. — The 1"5 volts are required to send J amp. through the 
resistance of 3 ohms. 

(7) Four resistances, two of 8 ohms each, one of 4 ohms, and one 
of 6 ohms, are placed in parallel with one another. 

(a) What is their combined resistance ? 

(b) What drop would take place in each resistance if 4 amps, 
were passed through the combination ? 

(0) What current would pass through each resistance ? 

3 _f- 3 4. 6 + 4 

(a) Combined conductivity = 1+1 + ^ +i= 9T = 24 

.*. combined resistance = f-| = IJ ohms 
Therefore the combined resistance of the set = 1^ ohms. 

(b) The same drop is bound to take place in each resistance 

when placed in parallel. 

Therefore if 4 amps, pass through the set, the drop taking place 
in any one resistance or in the set will be 4 x I'o = 6 volts. 

E 

(c) The current through each res. of 8 ohms, as C = p, will 

therefore = [: = f amp. 



42 ELEMENTS OF ELECTRIC TRACTION 

Current through the res. of 4 ohms ) ^ 

will therefore f = I = H amps. 

Current through the res. of 6 ohms 1 « ^ 

will therefore f = t = 1 amp. 

Total current then passing being ) . 

l + f+li+l f=^ ^°^P^- 

Therefore current passing through each resistance of 8 ohms 
= f amp. 

Therefore current passing through the resistance of 4 ohms 
= ij amps. 

Therefore current passing through the resistance of 6 ohms 
— I amp. 

(8) A resistance of 8 J ohms is placed in series with the 4 resist- 
ances in parallel in the above example. 

What current would flow if a battery with an E.M.F. of 3 volts 
and an internal resistance of 2 ohms was employed to send current 
through this particular arrangement of resistances ? 

Total effective E.M.F. = 3 volts 
Combined resistance of the 4 resistances = 1*5 ohms 
Eesistance in series with above = 8*5 ohms 
Internal resistance of battery = 2 ohms 
.*. total resistance in circuit =12 ohms 

E 

As C = p .-. C = ^2 = a amp. 

Therefore current flowing through the above arrangement would 
be i amp. 



CHAPTER IV 
PRINCIPLE OF THE DYNAMO 

While there are various methods of generating electricity, the only 
practical and economical method of generating such electrical pressures 
as are required for engineering and traction purposes, is by means 
of the dynamo or continuous-current generator where continuous 
currents are employed, or by means of an alternating generator 
where alternating currents are employed. The principle underlying 
both is the same. 

Fundamental Principle. — When dealing with electromagnetism 
it was seen that a current of electricity flowing along a conductor 
caused a magnetic needle suitably situated to move, this being due 
to the magnetic field set up by the current. 

It has also been found by experiment that a reverse effect can be 
somewhat similarly produced, namely, that a moving magnet will set 
up a difference of electrical pressure in a conducting wire suitably 
situated, the difference of electrical pressure causing a current to 
flow if a complete path be provided. In the one case a current of 
electricity causes a magnet to move, in the other a moving magnet 
causes a current of electricity to flow. If the conducting wii^e be 
suitably moved instead of the magnet, a difference of pressure will 
also in like manner be set up. 

To put this in its simplest form, suppose two bar magnets be 
taken (see Fig 11), and that the north pole of one be placed opposite 
the south pole of the other, a small distance separating them ; 
between these two poles there will be a fairly concentrated magnetic 
field. If now, say, a copper wire be taken and passed down through 
this gap between the poles, the wire being at right angles to the 
magnets so as to cut across the imaginary magnetic lines which are 
passing from the north to the south pole, it will be found there is set 
up a difference of electrical pressure between the ends of the copper 
wire, when the wire is passing down the gap, or, in other words, when 
cutting across these imaginary magnetic lines ; and if a suitable 
complete circuit be provided, this difference of pressure will cause a 



44 



ELEMENTS OF ELECTRIC TRACTION 



current to flow through the circuit. This current would, however, 
be exceedingly small, as the magnetic field would only be a weak 
one, and would require some very delicate instrument in order to 
detect it. If, now, instead of passin 



g the wire down between the 




Fia. 11. 



poles it is moved, say, simply from north to south, sliding as it were 
along these imaginary lines, and not cutting across them, it will be 
found that no electrical pressure whatever is set up ; an electrical 
pressure only being set up when these imaginary magnetic lines are 
cut across, or in two, as it were. 

The above indicates the fundamental principle upon which all 
dynamos are based. 

It will thus be seen that there are two essential parts and one 
essential feature for the production of electrical pressure in every 
dynamo. 

Essential parts — conductors and magnets. 

Essential feature — relative motion, a certain direction of motion 
being essential. 

The relative motion is that which must take place between the 
conductors and magnets ; thus to take two of the simplest cases, 
either the magnets could move and tlie conductors be stationary, or 
the conductors could move and the magnets be stationary. In most 
continuous-current dynamos the latter is the general practice. 

Electromotive Force. — The pressure of electricity generated it 
is found depends, not simply upon the number of imaginary magnetic 
lines, but upon the rate at which these , lines are cut, namely, the 



PRINCIPLE OF THE DYNAMO 



45 



number cut per second ; consequently the E.M.F. of a dynamo depends 
primarily upon three things — 

1. The strength of the magnetic field, that is, upon the total 
number of lines cut in one revolution. 

2. The speed at which the wires, or conductors, as they are 
called, move or cut across the field, that is, upon the number of 
revolutions per second. 

3. The number of conductors connected in series and which are 
engaged in cutting the lines. 

The reason for the last statement is, that as there are practical 
limits both to the speed and to the strength of the field, and also in order 
to obtain a more uniform pressure, it is the practice in all generators 
to have a number of conductors coupled up in series, so that the 
E.M.F. generated in one conductor is added to the E.M.F. generated 
in another, and so on. By this means, not only is a higher pressure 
more readily obtained, but also a more 
uniform one, as will be seen later. 

It will be noted in the simple 
experiment described, that the direction 
of magnetic force, namely, that pointing 
from north to south, direction of current 
(when there was a circuit for such), and 
direction of cutting motion, that is, either 
up or down, were all at right angles to 
one another, and experiments show that 
the exact relation between these three 
directions (see Fig. 12) can be repre- 
sented by means of the following right- 
hand rule : — 

Right - hand Rule. — Place the 
thumb and first two fingers of the right 
hand all at right angles to one another. 
Then place the thumb in the direction 
of the magnetic force, namely, pointing 
from north to south. Arrange the 
hand so that the second finger points 

in the direction in which the wire or conductor cuts the field, that is, 
either up or down, still keeping the thumb pointing from north to south, 
then the first finger will indicate the direction in which the electrical 
pressure generated tends to drive the current. 

Taking the simple case of the wire passing down between the 
north and south poles of two bar magnets, if the north and south 
poles be arranged as in Fig. 11, then, on passing a wire down 
between these poles, experiments show that an electrical pressure 
is generated, tending to send current along the wire from right to 




Fig. 12. 



46 



ELEMENTS OF ELECTRIC TRACTION 



left, as indicated by the arrow. If the wire be moved up the gap 
instead of down, the electrical pressure generated will tend to send 
current from left to right, namely, in the reverse direction. If, on 
the other hand, the direction of the field be reversed, namely, a north 
pole take the place of a south, and a south take the place of a 
north, and the wire be moved down, then current will tend again to 
flow in the opposite direction to that indicated by the arrow. Tlius 
reversing either the direction of motion, or reversing the direction of 
field, causes the pressure generated to be also reversed as regards 
direction. The finger rule given can in this way be checked. 

If now a complete rectangle of wire be taken, as shown in Fig. 13, 
and passed vertically down so as to cut across a uniform magnetic 




Fig. 13. 



field as shown, the conductors AB and CD will both cut these 
lines, and as they both cut them at the same rate, the same pressure 
will be generated in each. The wires AC and BD will not cut 
across the lines, but slide along them, consequently these would be 
of no use for generating electrical pressure, but would simply connect 
AB and CD together. Now in this case, as the pressure generated 
in AB would tend to send current one way round the rectangle, 
namely, from A to B, and the pressure generated in CD would tend 
to send current the opposite way round, namely, from C to D, no 
current would flow, seeing the pressures are equal and opposite. If, 
however, AB was cutting lines in a very dense field, and CD in a 



PRINCIPLE OF THE DYNAMO 47 

very weak one, namely, if the field was not uniformly strong, the 
pressure generated in AB would be greater than the pressure 
generated in CD, and current would then flow in that direction 
in which the greater pressure tended to send it. If, however, the 
rectangle be rotated, say in the direction of the hands of a watch, as 
indicated by the dotted lines, instead of being moved vertically down, 
then when AB was cutting down across the lines, CD would be 
cutting up, and the directions of the pressures would not then oppose, 
but would assist each other, current then circulating from A to B, 
and from D to C round the rectangle. During the next half- 
revolution, namely, when AB is moving up, and CD moving down, 
current would circulate round the rectangle from C to D and from 
B to A. It will thus be seen that continuous rotation causes current 
to flow first one way and then the other round the rectangle. 

The next feature of importance in any dynamo is that connected 
with the collection of the current from the various moving conductors, 
so that the pressure generated may be applied to some external 
circuit, and a complete path be so provided that current may flow 
from the dynamo through the external circuit back to and through 
the dynamo. In the simple rectangle shown in Fig. 13, the circuit 
was simply that of the rectangle or coil itself. 

Simple Dynamo — In Fig. 14 is shown in skeleton form the 
simplest possible form of dynamo. This consists, as will be seen, of 




Fig. 14. 



a single coil ; that is, two conductors suitably connected together, one 
conductor being connected at one end to a metal ring (slip-rings, as 
they are generally called), and the other conductor being connected 
to a similar ring. The two rings are insulated from one another, and 
the whole is fnounted on, and insulated from, a suitable spindle, so 



48 ELEMENTS OF ELECTRIC TRACTION 

that the coil can be rotated. Bearing on the rings are two contact 
fingers, or brushes, which conduct the current to the external circuit. 
When the coil is in the position shown, current will be passing out 
of the ring marked A, going through some external circuit, say, and 
returning back through the ring marked B, a complete circuit thus 
being provided not only from and to the dynamo, but also through 
the dynamo. By the time the coil has gone halfway round, or 
through 180°, it will be found that the conductor connected to ring 
A is cutting across the magnetic lines in the reverse direction ; 
also in a similar manner the one connected to B ; consequently, the 
pressure will be reversed, and hence the direction of current will also 
be reversed. In this way, current will flow first one way through 
the circuit, and then the opposite way. Such a current is called an 




Fia. 15. 



alternating current, and the arrangement shown in Fig. 14 is really 
the simplest possible form of an alternating generator. 

For most traction purposes continuous current is employed, and 
consequently a generator built on these lines would not be suitable 
for supplying current direct to the trolley wire. 

Referring now to Fig. 15, a different arrangement will be seen : 
one end of one conductor is connected to a half-metal ring, and the 
other conductor connected to another half-metal ring, the half-rings 
being insulated from one another. It will be seen from the figure 
that current is passing, when the coil is in the position sho^vn, 
from the half-ring A to the top brush, and from there through the 
external circuit back to the bottom brush, and so to the other half- 
ring B. On moving the conductors round halfway, namely, 



PRINCIPLE OF THE DYNAMO 49 

through 180° just as before, it will be noticed that the conductor 
connected to A will, owing to its new position, have the current 
reversed in it ; but the half-ring A connected to this conductor now 
no longer touches the same sliding contact or brush, but the opposite 
one, namely, the bottom one. Thus, in the simple case illustrated, 
the top brush, for instance, is only connected to a conductor while 
current is flowing through that conductor in one direction, and 
current will be flowing through the opposite conductor in this same 
direction when that conductor comes in contact with this same 
particular brush. A little thought will show that in this way 
current will always flow the same way round the external circuit. 
In this way a current is obtained which flows continuously in one 
direction, and such a current is called a continuous current. 

Uniform Pressure. — When the coil is in the position shown in 
the figure, the two conductors, it will be seen, are cutting directly 
across the magnetic lines ; they will then, in consequence, at that 
instant — assuming the speed to be constant — be generating the 
maximum E.M.F. Later, for instance, when the coil is in a position 
at right angles to that shown, the two conductors will be sliding 
aloncr the magnetic lines, and no E.M.F. at that instant will be 
generated. In the intermediate positions they will partly cut and 
partly slide. In this way, it will be seen the pressure generated by a 
single coil rotating in a uniform field will not be constant in value, 
but will vary, for instance, during one half-revolution in the 
following manner : — 

Starting from the instant when the pressure generated is at the 
maximum value, it will be seen that the pressure gradually decreases 
in value until it becomes nothing at all, then it gradually increases in 
value until the maximum pressure is again reached. During the next 
half-revolution it will vary in a similar manner. This is on the assump- 
tion that the speed has not varied in any way during the revolution 
considered. It must be noted that while the pressure varies in value, 
the direction the pressure is tending to drive current through the 
external circuit is always the same, owing to the arrangement of the 
two half-rings, or simple two-part commutator, as it is called. It 
may here be mentioned that in alternating work, not only does the 
pressure drive current first one way, then the other, through the 
circuit, but also it varies in value in a similar manner to that 
indicated above. In continuous-current work, however, dynamos are 
designed to give practically a constant pressure. This is obtained in 
the following manner : — 

If, iustead of two conductors, eight are taken, as indicated 
diagrammatically in Fig. 16, and connected to a four-part commutator, 
it will be seen that, with such an arrangement, when four of the 
conductors are idle, owing to their position, the other four will be 



50 



ELEMENTS OF ELECTRIC TRACTION 



generating. In this way a more uniform pressure can be obtained. 
In actual practice, to obtain practically a constant pressure, a number 
of conductors are arranged all round the armature core, with a 
corresponding number of commutator segments. By this means a 
large number of conductors are continually at work generating au 




e '7 

IN TH£ POSITION SHOWN 
I. 2. 5, and6 are ACTIVe CONDUCTORS. 

J,4,7,anp8v\re /dl£ conductors. 

Fig. 16. 



electrical pressure, and it will be noted when one conductor is passing 
into a worse position for cutting lines, another is passing into a 
better ; the result is that practically a constant pressure is obtained ; 
uniform direction being obtained, as previously explained, by means 
of the commutator. 

It should be particularly noted that all remarks previously made 
have been made with reference to continuous-current work, and not 
to alternating work. Ohm's law, for instance, as given, would not 
apply to alternating work. 

Construction. — The following description will indicate the most 
important features in the actual construction of a dynamo : — 

Commutator. — In actual dynamos, the two half-rings are 
replaced by a number of segments, owing to there being a number of 
conductors. This part of the dynamo is called the commutator, and 
the various segments, commutator bars or segments, the various 
segments being insulated from one another and from the rest of the 



PRINCIPLE OF THE DYNAMO 51 

machine generally by means of mica. The same principle holds 
good with a number of segments, as in the simple two-part 
commutator shown in Eig. 15. 

Brushes. — The contacts which bear on the segments are called 
the brushes. These brushes consist generally of specially prepared 
carbon blocks attached to suitable holders. It should be noted that 
at the instant when the brush is bridging across the segments, and so 
shortcircuiting that particular coil, the coil when in that position is 
not cutting across the lines of magnetic force, and consequently that 
particular coil at that instant will not be generating any electro- 
motive force, and so no damage is done by such shortcircuiting. In 
actual practice, however, it must be said, a great many difficulties 
are here introduced. 

Magnets. — In order to obtain strong magnetic fields, electro- 
magnets are employed, the current required for magnetizing these 
being obtained, as a rule, from the dynamo itself. The different 
types of dynamos are described by the particular methods of connect- 
ing the field coils to the armatures. Thus — 

Series Dynamo. — If the whole of the current passing out of 
the dynamo passes through the coils which are used for exciting or 
magnetizing the field, that is, if they are in series with the armature, 
then such is termed a series dynamo. 

Shunt Dynamo. — If, however, only a small fraction of the total 
current coming from the dynamo be employed for purposes of 
excitation, that is, if a small fraction of the total current be shunted 
through the field coils on the magnets, then such is termed a shunt 
dynamo, the field coils being connected as a shunt across the armature. 

Compound Dynamo. — A combination of the above two 
methods of winding the field is very often adopted, and such is called 
a compound dynamo. 

Separately Excited Dynamo. — If the terminals of the field 
coils of a shunt dynamo be disconnected from the armature, and the 
current from the field be taken, not from the dynamo itself, but from 
some separate source, then such a dynamo is said to be separately 
excited, as compared with the self-excitation of other dynamos. 
The behaviour of such a dynamo is very similar to that of a shunt 
dynamo. 

In the shunt dynamo, as the exciting current is only small, a 
great many turns of wire are employed in order to get the requisite 
ampere turns, the wire in this case, having only a small current to 
carry, is only of small section. In the series dynamo, as the exciting 
current is the full current the machine is giving, less number of 
turns are required, and these of large section. 

Armature Core. — The core upon which the conductors are 
wound is called the armature core, and is generally made of soft iron, 



52 ELEMENTS OF ELECTRIC TRACTION 

for the purposes of concentrating and providing an easier path for the 
magnetic lines. Now, just as an electrical pressure is set up in the 
conductors, so an electrical pressure would be set up in this rotating 
iron core, producing current, which would simply circulate down one 
side and up the other of the core. This would heat up the iron core, 
and energy would be wasted. To prevent this, the armature is not 
made of solid iron, but is built up generally of thin circular charcoal 
iron sheets, these being varnished or papered, and thus insulated one 
from the other. This building up of the armature by means of thin 
sheets or laminae is called laminating the armature core. The in- 
sulating of these various sheets one from the other directly prevents 
these eddy currents, as they are called, circulating through the core, 
and thus prevents energy being wasted. The core, however, will 
still provide a path for the magnetic lines of force, the laminating of 
the core in no way interfering with this. 

In tramway motors, and also in most large dynamos, slots are 
cut out of the armature, and in these the conducting wires are em- 
bedded. The benefit of tliis, from a mechanical point of view, is that 
the conducting wires are firmly fixed to the armature, as, in the case 
of a motor, for instance, it is the action between the field and the 
currents w^hich the conductors are carrying which causes the arma- 
ture, and hence the shaft, to rotate ; consequently the need for the 
conductors to be firmly attached in order to transmit the necessary 
driving force. 

Armature Conductors. — As already mentioned, a great number 
of conductors or coils are employed. These conductors generally con- 
sist of copper wire or bars, suitably insulated from the armature core 
and from one another, the conductors at one end being connected to 
the various commutator segments. Copper is employed because of 
its good conductivity, less heat in this way being generated in the 
conductor, and consequently less energy wasted. 

Characteristic Properties. — Investigations have shown that 
the various types of dynamos behave differently, or, as is generally 
stated, have different characteristics. 

On testing a dynamo to find out its characteristic, no attempt is 
made to regulate the dynamo, as the object is to see how the dynamo 
regulates itself; consequently, in taking the characteristic of any 
dynamo, it is run at a constant speed, and the shunt regulator in a 
shunt machine is not interfered with while the test is being made. 

The following notes will just briefly indicate the chief charac- 
teristics of the various types : — 

Shunt Characteristic. — A shunt dynamo, when tested, will be 
found to give its full voltage when no current is flowing through the 
external circuit ; in other words, when the dynamo is on open circuit. 
It should be noted the only current then passing through the dynamo 



PRINCIPLE OF THE DYNAMO 53 

is the small current that will be passing through the field coils. On 
closing the external circuit, and gradually loading the dynamo up by 
reducing the resistance in the external circuit, so that the current is 
gradually increased, it will be found that as the current increases the 
volts decrease. This decrease, however, is not a very great one, 
within the ordinary limits of full load. In a well- designed shunt 
dynamo the drop in pressure will probably be some 10 per cent, of 
the full voltage. Such a dynamo is said to have a falling charac- 
teristic, as the volts fall as the current is increased. It may be 
mentioned that shunt dynamos, as a rule, are fitted with shunt 
regulators, and by means of these the current passing through the 
field coils can be regulated, and in this way the magnets can either 
be strengthened or weakened. By this means the volts caii either be 
increased or decreased within certain limits. 

Series Characteristic. — A series dynamo, when tested, will be 
found to give on open circuit only a very small voltage. The reason 
for this is that when this type of dynamo is on open circuit no 
current is passing through the field coils, as they are in series with 
the armature, and not in parallel, as is the case with the shunt 
dynamo. The voltage thus obtained with a series dynamo on open 
circuit is simply that due to the residual magnetism of the field 
magnets, and this will only be a very small part of the total generated 
later when on full load. On closing the circuit and gradually re- 
ducing the resistance in the external circuit, it will be found that the 
machine will not build up, as it is termed ; that is, no definite pres- 
sure will be maintained, and no appreciable current will flow unless 
the resistance be reduced to a certain amount. Finally, when the 
resistance is reduced so that an appreciable current begins to flow, it 
will be found that as the dynamo is loaded up — the current being 
increased by reducing the resistance — the volts, within certain limits, 
will also increase. Such a dynamo is said to have a rising charac- 
teristic, as the volts rise in value as the current is increased — that is, 
within certain limits. 

Compound Characteristic. — A compound dynamo, when tested, 
will be found to give practically a constant voltage at all ordinary 
loads. This is brought about by the combination of series and shunt 
windings. As a rule, such machines are designed either to give a 
constant voltage, or a slightly increasing voltage with increase of load. 

The following reasons will briefly indicate why the above results 
are obtained : — 

In a shunt dynamo the field becomes weaker the greater the 
current passing through the armature ; the result is, the greater the 
current the less the E.M.F. generated. This weakening of the field 
is due to two causes, one of which is brought about indirectly and 
one directly — 



54 ELEMENTS OF ELECTRIC TRACTION 

1. In every dynamo certain demagnetizing actions are set up, 
due to the current circulating round the armature core, which de- 
magnetizing action tends to weaken the main field. The greater the 
current passing through the armature the greater the demagnetizing 
action set up, and, consequently, the greater the current the weaker 
the field. 

2. The current through the field coils, and hence the strength of 
the magnetic field, depends upon the P.D. across the terminals of the 
field coils. This P.D. depends not only upon the E.M.F. generated, 
but also upon the " drop " taking place in the armature, and the 
greater the current the greater will be this drop. 

The result of these two actions is, that not only is the field 
weakened indirectly by means of the demagnetizing action, but it is 
also weakened directly due to the decreased current through the field 
coils, which is the outcome of the lesser E.M.F. generated, and the 
increased drop taking place in the armature with increase of load. 
Within the limits of ordinary load the total drop is, however, not a 
great amount in a well-designed machine, as already mentioned. 

It should be noted that even if the E.M.F. generated were always 
constant, there would be a slight drop in the terminal volts as the 
current was increased, due to the drop taking place in the armature, 
this increasing with increase of current. 

In a series dynamo, as the current increases the field will also 
increase in strength, and while the demagnetizing action will tend 
somewhat to weaken it, the field as a whole will increase in strength, 
and the E.M.F. will correspondingly increase with increase of 
current. Later on, with heavy loads and with saturated magnets, the 
demagnetizing action may cause the volts to drop. The P.D. across 
the terminals in this, as in all other dynamos, will be less than 
the E.M.F. by the amount of the drop taking place in the armature, 
and in this case the field coils. 

In a compound dynamo sufiicient series turns are generally added 
to what is practically a shunt dynamo, to approximately give the 
necessary increase in volts to make up for the drop due to the 
various causes. In this case the field coils will consist of two sets, 
one taking a small fraction of the total current, and the other 
consisting of a few turns taking the whole of the current. 

It is on account of the magnetizing effects due to current in the 
armature that the brushes have to be moved round in a dynamo in 
the direction of rotation, and in motors in the reverse direction, in 
order to prevent sparking at the commutator. Tramway motors, 
however, are designed for a fixed position of the brushes. 

Finally, it must be remembered that all self-exciting dynamos 
have to depend upon the residual magnetism of the field magnets for 
generating an E.M.F. on starting up, as, until a current begins to 



PRINCIPLE OF THE DYNAMO 55 

flow, the machine will not be excited electrically. The initial 
current is obtained by means of the weak residual magnetic field. 
The building up of the full field then takes place if the conditions 
are suitable ; that is, neither too large a resistance in the shunt 
circuit of a shunt dynamo, nor too large a resistance in the main 
circuit of a series dynamo. 

Motive Power. — It must always be remembered that power will 
have to be supplied to the dynamo in order to drive it, a force being 
required to pull the conductors round when they cut across the 
magnetic lines of the field, that is, when current is flowing. The 
greater the output of the dynamo the greater the power required to 
drive it. But it should be noted that when no current is flowing, no 
pressure or force will be required to move the conductors other than 
that required for overcoming the mere friction, etc., so that when no 
electrical power is being generated no power will be required to 
drive the dynamo, other than that required to overcome the friction 
of tlie bearings, brushes, etc. The force which will have to be exerted 
on the conductors to twist the armature of a dynamo round will 
depend primarily upon (1) the intensity of the field, (2) the current 
flowing through the armature conductors, and (3) the number and 
length of the conductors. While outwardly there is nothing to 
indicate there would be any resistance to twist the armature round, 
it must be remembered that the forces simply have no visible 
medium. 



CHAPTER V 

PRINCIPLE OF THE CONTINUOUS-CURRENT 

MOTOR 

Fundamental Principle. — When dealing with the principle of the 
dynamo, reference was made to a fundamental experiment in electro- 
magnetism. That same experiment will now again be referred to in 
dealing with the principle of the motor. The experiment showed 
that if a wire through which a current of electricity was passing was 
placed over and near a magnetic needle, the needle was deflected, 
that is, it moved under the action of some force, namely, a magnetic 
one, a magnetic field being set up by the current of electricity flow- 
ing through the wire. Now, the force between the magnetic needle 
and the wire carrying the current was a mutual one ; that is, that 
just as a force was at work tending to move the needle, so also an 
equal and opposite force was at work tending to move the wire. In 
the experiment referred to, the wire was held and the needle moved ; 
had the needle been held, and the wire quite free to move, then the 
wire in this particular case would have twisted or deflected in the 
opposite direction to that taken by the needle. 

A simple experiment will still further illustrate this — 
One end of a conducting wire, AB (see Fig. 17), was hooked on 
to a conducting and supporting wire leading from a set of batteries. 
The other end, B, of the wire dipped into a glass vessel containing 
water, to which a little acid was added to make the water conduct 
somewhat better. The circuit was completed by running another 
wire from the water back to the battery, a switch being placed in 
the circuit. In this way, current could be passed through the wire 
AB, which was free to swing. A couple of bar magnets were fixed 
as shown, thus placing a portion of the wire in a magnetic field. 
Experiments then showed that on passing a sufficiently large current 
through the circuit, the wire moved either towards or away from the 
reader, depending upon the direction current was passing through the 
wire, namely, up or down. Had the wire not been hinged at the end 
A, but free to slide altogether, it would have tended to move bodily 



PRINCIPLE OF THE CONTINUOUS-CURRENT MOTOR 57 

either towards or away from the reader. Again, had the north pole of 
one of the magnets been placed dead over one end of the wire AB, and 
the south pole of the other bar magnet dead under the other end of 
the wire, no motion would have taken place. Motion of the wire only 
takes place when by so doing it cuts across magnetic lines of force. 
In the experiment as originally described above, the magnetic lines 
of force were cut as the wire moved. With the magnets placed dead 



e^ 



<9. 



N 



J 



S 



^5= 



I 



t 






BATTERY 



Fig. 17. 



over and under the wire, that is, when the direction of the current 
and direction of field are exactly in line, any slight motion of the 
wire, it will be seen, either up or down, sideways, backwards, or 
forwards, only causes the wire to slide along the lines, and cutting 
does not take place, and hence in this case no motion would take 
place. It will therefore be seen that there are two essential parts, 
and one essential feature, in every continuous-current electric 
motor, namely — 

Essential Parts — conductors and magnets. 

Essential Feature — current must flow through the conductors, 



58 ELEMENTS OF ELECTRIC TRACTION 

a certain position of the conductors with regard to direction of field 
being essential. 

The resulting motion could either be that of the magnets or that 
of the conductors. In actual practice the magnets are stationary, 
and the conductors move, the armature to which they are fixed 
rotating. 

It will thus be seen that the essential parts of a motor are the 
same as those of a dynamo, and an electric motor in its construction 
is identical in every respect with a dynamo. In the dynamo the 
conductors are moved and an electromotive force is generated. In 
the motor an electromotive force is applied so that current flows 
through the conductors, and a force is set up which tends to move 
the conductors. Any motor, if driven from some suitable source of 
supply, such as a steam-engine, will generate an electrical pressure, 
and any dynamo, if supplied with a suitable current, will run as a 
motor. Certain details, such as direction of rotation, will have to 
be seen to, etc., but these in no way affect the general principles 
laid down. Thus it will be seen, in the dynamo, mechanical energy 
is supplied and electrical energy generated ; in the motor, electrical 
energy is supplied and mechanical energy generated. 

The motion of a conductor carrying a current of electricity in a 
magnetic field can also be experimentally shown by means of a con- 
tinuous-current arc light. It must be explained that the excessive 
heat which is developed when an arc of any kind is formed, causes 
the metal — or carbon in the case of an arc light — to be vaporized and 
burn, also that the burning vapour acts as a conductor. This ex- 
plains why an arc once formed is so readily maintained. If the arc 
be placed in a suitable magnetic field it will be found that the 
conductor — in this case not a wire but the burning vapour — moves 
just as the wire did. This causes the arc to be displaced, and conse- 
quently lengthened, and in this way to be " blown out ; " the 
lengthening of the arc increasing the resistance, thus reducing 
the current, and consequently the heat, and, with the reduction of 
the heat, the reduction of the arc. 

The above is the principle adopted in the magnetic blow-out, a 
strong magnetic field being so arranged as to blow out any arc formed 
on breaking the circuit. 

Driving Force. — The force tending to rotate the armature of a 
motor, that is, the sum of the forces acting on all the conductors, it 
is found depends primarily upon three things — 

1. The intensity of the magnetic field, that is, upon the density 
of the magnetic lines. 

2. The current flowing through the conductors. 

3. The number and length of conductors actively employed. 
From this it will be seen that in any given motor the force 



PRINCIPLE OF THE CONTINUOUS-CURRENT MOTOR 59 

tending to rotate the armature will primarily depend — as the number 
and length of conductors will always be the same — upon the strength 
of the magnetic field and upon the current passing through the arma- 
ture conductors. The greater the current and the more intense the 
field, the greater will be the force acting. 

It will be noted in the simple experiment described that the 
direction of magnetic force, namely, that pointing from north to 
south, direction of current and direction of motion were all at right 
angles to one another, and experiments show that the exact relation 
between these three directions can be represented by the following 
Left-hand Eule : — 

Left-hand Rule. — Place the thumb and first two fingers of left 
hand all at right angles to one another. Then place the thumb in 
the direction of the magnetic force, namely, pointing from north to 
south. Arrange the hand so that the first finger points in the 
direction in which current is passing through the conductors, still 
keeping the thumb pointing from north to south, then the second 
finger will indicate the direction in which the conductor will tend 
to move. 

The above left-hand rule enables the direction of motion of a 
conductor in a motor to be determined, if direction of field and 
direction of current be known, just as the right-hand rule enables 
direction of current through a conductor in the case of a dynamo to 
be determined, where direction of field and direction of motion are 
known. 

Referring now to Fig. 17, it will be seen that if current passes 
down the wire, that is, from A to B, the wire will tend to move towards 
the reader; if the connections to the battery be reversed, so that 
current passes up instead of down, the wire will tend to move away 
from the reader. If, now, the field be reversed, the north pole being 
placed at the right-hand side, and the south at the left, and current 
be passed down the conductor, its tendency will be to move away 
from the reader. Thus, reversing either the direction of current or 
direction of field causes the motion to be reversed. To reverse, 
then, the direction of rotation of a motor, either its field must be 
reversed, or direction of current through the armature conductors 
must be reversed. 

In dealing with the dynamo, a commutator was found to be neces- 
sary to enable the current passing through the conductors to flow 
always in one direction through the external circuit. This being due 
to the fact that with the armature rotating continuously in one direc- 
tion, current flows first one way and then the other through any one 
conductor, in consequence of it both cutting up and cutting down, 
across the lines of the magnetic field. 

In the motor, the commutator has to fulfil just the opposite 



6o ELEMENTS OF ELECTRIC TRACTION 

purpose, namely, to enable the continuous current supplied to flow 
first up and then down any one conductor, depending upon its position 
in the field, and in this way enabling continuous rotation of the 
armature to be obtained. 

In the one case the commutator was required to obtain con- 
tinuous current with continuous direction of rotation, and in the other 
with continuous current to obtain continuous direction of rotation, 
constant direction of field being assumed as is actually the case 
with continuous-current motors and generators. 

A reference to Figs. 14 and 15, and an application of the above 
left-hand rule, will more definitely show this need of a commutator 
in order to obtain rotation in one continuous direction. 

Back Electromotive Force. — A most important point in con- 
nection with motors is that dealing with what is called the back 
electromotive force. 

Before attempting to explain this, the following facts will first of 
all be considered : — 

A small series motor was taken, and the resistance of the armature 
and field — the field in a series motor being in series with the armature 
— was measured and found to be, roughly speaking, about 1^ ohms. 
Now to send, say, for example, 3 amps, through a resistance of 1 J ohms, 
a pressure it will be seen of 3 X IJ, namely, 4^ volts, would be 
required. Actually, however, a pressure of 100 volts, about twenty- 
two times the above pressure, is applied to the terminals when the 
above motor is running under ordinary working conditions. With 
twenty- two times the applied pressure, if the resistance in the circuit 
— namely, under working conditions the resistance of the armature 
conductors and field winding — had only to be considered, twenty-two 
times 3 amps., namely, some 66 amps., would fiow through the motor 
circuit. As a matter of fact, however, experiments show that when 
the motor is running on a light load, only some 3 amps, pass through 
the circuit, but that if friction be applied to the motor pulley so as to 
reduce the speed, the current increases ; in fact, the current increases 
as the load upon the motor is increased. 

It will be seen from the above that something else besides the 
resistance of the motor and the applied voltage has to be considered 
in determining the current passing through a motor, and that some- 
thing depends upon the motion of the armature. So much does the 
current depend upon the motion, that if the armature of the above 
motor is held so that it cannot rotate, experiments show that a 
pressure of 4 J volts is quite sufficient to send a current of 3 amps, 
through the armature and field, thus indicating that a pressure of 
100 volts under similar conditions would send the excessive current 
of 66 amps, through the armature and field, which, as a matter of 
fact, is nearly 4 J times the maximum current, namely, 15 amps., 



PRINCIPLE OF THE CONTINUOUS-CURRENT MOTOR 6i 

this particular motor is designed to carry. In contrast, then, with 
the current of 66 amps., one has to consider the 3 amps, passing 
through the motor under exactly the same condition as regards the 
resistance in circuit and applied voltage, the sole difference between 
the two cases being that in the one case the armature is at rest, and 
in the other the armature is in motion. 

The explanation of this is as follows : — 

When dealing with the principle of the dynamo, it was seen that 
two essential features, namely, conductors and a magnetic field, and 
one essential condition, namely, relative motion, were necessary for 
the production of electrical pressure. Now, in a motor in motion, 
all these conditions are fulfilled, so it is practically a dynamo in 
motion, the particular motive power causing rotation ; that is, v/hether 




Fig. 18. 



it is being rotated electrically, or by hand, or by whatever means, 
making no difference, the fact remains the armature is in motion and 
the field is excited. Consequently, the motor, when running, will 
generate a pressure of electricity just as any dynamo would, and this 
pressure will tend to send a current of electricity in a certain direction 
through the circuit. 

On taking the simplest possible case (see Fig. 18), it will be 
seen that if the brush marked A be connected to the positive 
terminal of some source of supply so as to send current through 
the conductors from brush A to brush B, current will pass from 
C to D and from E to F. The motor will then run, it will be found, 
on applying the left-hand rule in the direction shown, namely, in 
the same direction as the hands of a watch. If, now, the motor be 



62 ELEMENTS OF ELECTRIC TRACTION 

looked upon as a dynamo, it will be found, on applying the right-hand 
rule, that when the conductors rotate in the direction shown — the 
field, of course, being still the same, as one is studying what is going 
on in the conductors at one and the same time — a pressure is 
being generated tending to send current in the reverse direction ; that 
is, from F to E and from D to C. The pressure generated, in short, 
will be found to oppose the applied pressure, and this opposing or 
back pressure is called the back electromotive force, briefly, the 
back E.M.F. The back E.M.F, will always be less than the applied 
E.M.F., because if they became equal, for instance, there would be 
no effective pressure, and no current would flow. The force driving 
the armature round would cease, and as the speed became reduced in 
consequence, so also would the back E.M.F. become reduced ; in 
other words, the back E.M.F. would not remain equal to the applied 
E.M.F. For the motor to generate a greater E.M.F. than the applied 
E.M.F., it must act no longer as a motor receiving electrical energy, 
but as a dynamo delivering electrical energy, power in this case being 
supplied from some source to drive it. 

To determine, then, the current in a circuit of this kind, the total 
effective pressure that is acting must be taken. In the case of a motor, 
the effective pressure is the difference between the applied and the 
back E.M.F., and it is this difference, divided by the resistance of 
the armatiu'e and field in the case of a series motor, which gives 
the value of the current. Thus in the above case, when 100 volts 
were applied to the motor terminals, and 3 amps, were flowing 
through the circuit, as only 4^ volts were required to send this 
current, a back E.M.F. of 100 minus 4^, namely, 95J volts, was 
being generated. 

The E.M.F. generated in any given motor, that is, the back E.M.F., 
will primarily depend, just as the E.M.F. of any given dynamo does, 
upon (1) the strength of field, (2) upon the speed of rotation, and (3) 
upon the number of conductors connected in series, and which are 
actively employed. 

The generation of a back E.M.F. raises up a very important point 
in connection with the starting of motors. When starting a motor, 
since the armature is at rest, no back E.M.F. will at the moment of 
starting exist, and consequently, were the full voltage to be applied 
directly to the terminals of the motor, and no other resistance in- 
serted in the circuit, an excessive current, as already seen, would 
flow. This excessive current would either blow the fuse or automatic 
cut-out placed in the circuit to protect it, or else, before the motor 
had time to get up speed and generate a back E.M.F., would cause 
serious overheating of some part of the circuit to take place, the out- 
come of which might either damage the insulation or burn the circuit 
out. When once a back E.M.F. is generated the current would be 



PRINCIPLE OF THE CONTINUOUS-CURRENT MOTOR 63 

reduced, depending, of course, upon the value of the back E.MT., as 
this would reduce the effective E.M.F. 

For example, as already stated, the current that would flow in 
the case of the small series motor, which has already been considered, 
under these conditions would be about; 4^ times the full-load current. 
As the heating depends upon the square of the current, in a given time 
over 4i X 4 J, that is, over twenty times more heat, would be generated 
than with full-load current. In a large motor the armature and 
field resistance will be much less than is the case with a small motor, 
and the result will be correspondingly and detrimentally greater. 
In order, then, to keep the current within reasonable limits on starting, 
a starting switch is provided, by means of which resistance can be 
inserted in the motor circuit, the resistance being made sufficiently 
great to keep the current within reasonable limits. Thus, if in the 
example above, 5 J ohms be inserted in series with the armature 
and field, this 5 J ohms, together with the IJ ohms due to armature 
and field resistance, will make a total of 7 ohms. Now, 100 volts 
will only send a little over 14 amps, through a resistance of 7 
ohms. In this way the starting current can be kept within any 
desired amount. As the motor gradually gets up speed, and so 
gradually generates a back E.M.F., so also can the resistance be 
gradually taken or cut out of the circuit by means of the starting 
switch, so that finally, when the motor has attained its full speed 
and so developed its full back E.M.F., all the resistance can and will 
be cut out. This does not necessarily mean the motor's highest 
speed, as in the case of tramway motors there are two speeds, one 
when the motors are in series, each getting only half-the-line voltage, 
and another when the motors are in parallel, each then getting the 
full-line voltage. In the intermediate positions, the current will 
be kept within reasonable limits, partly due to the resistance 
in circuit, and partly due to the back E.M.F. that is then being 
generated. 

In tramway work, the controller, besides fulfilling other functions, 
forms the starting switch for the motors. It is essential, then, that 
a motor should be provided with some suitable form of starting 
switch, and it is also equally essential in stopping a motor to see 
that the starting switch is moved back to its original or starting 
position, otherwise it may by carelessness be rendered of no use. 
Thus, if a motor is stopped by some other switch than the starting 
one — say by means of the main switch, the starting switch being left 
in its " ou " position — the next time the motor is started, the main 
switch might in all probability be inserted without attention being 
given to the starting one, in which case the starting switch would be 
rendered entirely useless for the purpose it was intended, being in its 
on position and having all the resistance in consequence cut out. 



64 ELEMENTS OF ELECTRIC TRACTION 

In order to guard against this, and to prevent accidents due to such 
carelessness, the starting switch is often made automatic, so that it 
always flies back to its starting position if the circuit is broken 
either directly, by means of another switch, or by means, for instance, 
of a fuse blowing. 

It may be mentioned in connection with traction work, that 
previous to making connection with the trolley wire by means of the 
trolley pole, care should be taken to see that the power handle of the 
controller is in the off position, not only for reasons similar to that 
given above, but also as accidents have happened owing to the car 
being in this way violently started with no one on board. 

In the ordinary type of tramway controller, such as the KIO, 
B13 (B.T.H.) etc., there is no attempt made to make the action 
automatic in the exact way as above mentioned, but the reverse, and 
power handles (that is, the barrels which they operate) are interlocked 
so that when all is in order, a man is bound to bring his power handle 
to the *'off " position or starting end, looking at it from the point of 
view of a starting switch, before he can bring his reverse handle either 
into its off position or to its reverse position. It may be said it is 
only when the reverse handle is in the off position that the operating 
reverse handle can be removed. 

By means of this interlocking arrangement, a man cannot break 
the circuit by means of the reverse handle until the power handle is 
in its proper position, namely, the off position. In fact, as far as the 
controller is concerned, he is bound to stop the motor by means of 
the starting-switch portion of the controller. 

In a similar way the power handle cannot be moved and resistance 
cut out without having first completed the circuit by means of the 
reverse handle. In short, as far as the controller is again concerned, 
a man cannot first cut out resistance and then complete the circuit 
through some other switching arrangement, namely, the reverse barrel. 

In this way the operations are bound to be performed in the right 
order, but it should never be forgotten that while reverse and power 
handles are interlocked, power handle and either trolley pole, canopy 
cut-out, or main switch are not interlocked, and here care and thought 
must be taken for the prevention of accidents. As already mentioned, 
before connecting trolley pole to trolley wire, or before closing canopy 
cut-out or main switch, it should always be seen that the power 
handle, or, more strictly speaking, the power barrel, is in its off 
position. 

Another advantage of the above interlocking of the two handles 
is, that as the man has but one reverse handle as well as one power 
handle, he is bound to bring the power handle to the right position 
before he can remove for use at the other end of the car the reverse 
handle. This will leave the barrels in the one controller not in use 



PRINCIPLE OFTHE CONTINUOUS-CURRENT MOTOR 65 

in their right position, and also prevents the controller barrels being 
tampered with. 

Cases are on record, where, owing to defective fitting, reverse 
handles have been removed when not quite in the off position ; the 
above remarks are on the understanding that all is in proper order. 



Examples 

(1) A pressure of 500 volts is applied to the terminals of a series 
motor. The resistance of the armature winding is 0*36 ohm, and 
the resistance of the series field winding is 0'76 ohm. 

What will be the back E.M.F. generated when a current of 
50 amps, is passing through the motor ? 
Effective pressure required — 

As E = CR = 50 (0-36 + 0-76) = 50 (M2), namely, 56 volts 
.-. back E.M.F. = 500 - 56 = 444 volts 

Therefore the back E.M.F. generated under above conditions is 
equal to 444 volts. 

(2) What current would pass through the above motor if all 
starting resistance were cut out before motion took place ? 

Effective pressure in this case = 500 volts, as there is no back 

E.M.r. 

As C = ^ .-. current = pr^ = 446*4 amps., say 446 amps. 

Therefore the excessive current of 446 amps, would pass through 
the motor under such conditions, that is, until motion began to take 
place. 

(3) The armature resistance of a shunt motor is ^ ohm, the 
pressure of supply is 500 volts. 

What resistance must be inserted on starting to limit the current 
to 60 amps. ? 

E 
C 
Total resistance required = 8"3 ohms 
.*. res. to be inserted = 8*3 — 0*5 = 7'8 ohms 

Therefore resistance to be inserted on starting = 7*8 ohms. 



As R = =! .-. R = %o_o = 8-3 ohms 



(4) Two series motors are placed in series with one another and 
in series with a starting resistance of 3*2 ohms. The combined 
resistance of the armature and field of each motor is 093 ohm, and 
the pressure of supply is 500 volts. 

V 



66 ELEMENTS OF ELECTRIC TRACTION 

What current will pass through the motors when each is 
generating a back E.M.F. of 150 volts ? 

Pressure of supply = 500 volts 
Total back E.M.F. = 150 + 150 = 300 volts 
/. effective pressure = 500 - 300 = 200 volts 
Total resistance in circuit = 3-2 + 0-93 + 0*93 = 5-06 ohms 

"p 200 

As C = ^ .*. current = ^-:r^ = approximately 40 amps. 

Therefore the current passing through the motors in the above 
case will be 40 amps. 

(5) Two series motors exactly similar to above are placed in 
parallel with one another, but in series with a resistance of 1 ohm, 
the pressure of supply being as before — 500 volts. 

What current will pass through each motor if each generates a 
back E.M.F. of 350 volts ? 

Effective pressure driving current through the resistance and 

the two motors in parallel = 500 — 350 = 150 volts. 
As the current passing through the resistance divides, only half 

the total current will pass through each motor. 
.*. 2CE la " drop '* in resistance, where C = current through 

each motor and E = value of the starting resistance. 
Also Cr = " drop " in armature of one motor, where r = 
resistance of armature and field winding. 
.*. 150 volts = 2CE 4- Cr 
.-. 150 „ = 2C (1) + C (0-93) 
/. 150 „ = 2C + 0-93C = 2-93C = say 3C 
/. 150 = 3C 
/. C = 50 amps. 

Therefore current passing through the resistance = 100 amps. 
Therefore current passing through each motor = 50 amps. 

(6) What back E.M.F. would each motor generate in the above 
case if 80 amps, were passing down the trolley ? 

Pressure of supply = 500 volts 
" Drop " in starting resistance = CE = 80 X 1 = 80 volts 

.-. pressure across terminals of I goo _ 80 = 420 volts 
each motor j 

Pressure required to drive 40) ^>,-r, ^nvnno Q^7o i+ 
,1^1 x^ . > = CE = 40 X 0'93 = 37 2 volts 

amps, through each motor ) 

/. back E.M.F. of each motor = 420 - 37-2 = 382*8 volts 

Therefore under above conditions each motor will generate a back 
E.M.F. of 382-8 volts. 



CHAPTER VI 
POWER AND POWER MEASUREMENT 

Before dealing with the actual measurement of either the electrical 
power supplied to a motor, or the mechanical power that the motor 
is capable of exerting, certain general principles of mechanics 
underlying the measurement of power generally will first of all be 
explained. 

Principle of Work. — If a weight of 1 lb. is lifted 1 foot high, 
1 foot-lb. of work is said to have been done. This is also expressed 
sometimes by saying that 1 foot-lb. of energy has been expended in 
raising 1 lb. 1 foot high. Consequently, if a weight of 1 lb. be lifted, 
say, first 1 foot high, then another 1 foot high, and then again another 
1 foot high, raising it in all 3 feet, a total of 3 foot-lbs. of work will 
have been done in raising the 1 lb. weight 3 feet high. If, instead of 
1 lb., three separate weights of 1 lb. each be lifted 1 foot high, it 
will be seen that exactly the same amount of work will have been 
done in lifting these three weights as in the previous case, namely, 
3 foot-lbs. If, now, the three separate weights be fastened together, 
and the whole three be lifted 1 foot high, exactly the same amount 
of work will have been done in raising the 3 lbs. all together as was 
done in lifting the three weights separately. Therefore the same 
amount of work is done in lifting 1 lb. 3 feet high as is done in lifting 
3 lbs. 1 foot high. 

If, instead of lifting a weight of 1 lb., a small truck had been 
moved a distance of 1 foot, which resisted motion in the direction it 
was moved with a force equal to that of a 1 lb. weight, then, in like 
manner, 1 foot-lb. of work would have been done in so moving it. 
The energy expended, expressed as so many foot-lbs. of work done, 
can thus be calculated — 

Hide. — Multiply the distance in feet a body is moved by the 
number of pounds' force resisting motion in that direction, and a 
number will be obtained expressing the number of foot-lbs. of work 
^one in so moving it. 

Conservation of Energy. — There is one great principle in 



68 ELEMENTS OF ELECTRIC TRACTION 

connection with energy, which is called the conservation of energy, 
which acts as a guiding principle in all engineering work. Stated 
briefly, this principle is that energy can neither be created nor 
destroyed. Practically it means — to take a simple case — that if so 
many foot-lbs. of work have to be expended in raising a body, at 
least that same number of foot-lbs. of energy will have to be exerted. 

With regard to the creation of energy, it may be pointed out that, 
for instance, in the case of coal, the heat energy is stored up in the 
coal, this energy having been derived ages ago from the sun. 

With regard to the destruction of energy, it should also be pointed 
out that the energy expended in any given case may or may not be 
readily available for use again. In most cases it is not, the energy 
expended not having been destroyed, but lost as far as all useful 
purposes are concerned. For instance, energy spent in overcoming 
friction is generally converted into heat, and this heat energy 
generally becomes dissipated and lost. If, however, to take a very 
simple case, a 10 -lb. weight be lifted 10 feet high, the 100 foot -lbs. 
of work which will have been expended in so raising it — neglecting 
the work done in overcoming friction — will be stored up in the 
w^eight, as it were, simply by virtue of its position, and this energy 
will be available for use again. The weight, for instance, could be 
allowed to fall again, and in so doing raise other weights up, a certain 
loss of energy, however, taking place in the process, due to friction, 
etc. This principle is sometimes practically employed in cable 
traction systems, cars descending inclines assisting cars which are 
ascending. 

While energy cannot be created or destroyed, it may be transferred 
or transmitted from one body to another body. Also energy of one 
kind can be transformed into energy of another kind, as, for instance, 
in the case of a dynamo, where mechanical energy is transformed into 
electrical energy, or, as in the case of a motor, w^here electrical energy 
is transformed into mechanical energy. 

From the above principle it will be seen that to do 3 foot-lbs. of 
work, 3 foot-lbs. of energy must at least be expended, and if by any 
mechanical arrangement, such as a lever, to take a simple case, a 
large weight is lifted by means of a small one, the distance the large 
weight is moved is correspondingly less than the distance the small 
weight or force is exerted, the work done being equal to the work 
actually expended, provided there is no friction or loss of any kind ; 
and where there is friction, then the work actually done is less than 
the work or energy expended, as part of the energy will be expended 
in overcoming friction — that is, it will be transformed or spent in the 
form of heat, which is useless for the purpose under consideration. 
Energy, as a matter of fact, is always lost (not destroyed), that is, as 
far as useful purposes are concerned, either in its transmission from 



POWER AND POWER MEASUREMENT 69 

one body to another, or in its conversion from one kind of energy to 
another, friction and other losses always occurring. 

Power or Rate of doing Work. — Up to the present, in dealing 
with work done, nothing has been said with reference to the time 
taken ; total work done has simply been dealt with, and not the 
rate or the speed, as it were, at which the work has been done, 
namely, the number of foot-lbs. of work done, say, in one minute. 
Now, the rate at which work is done expresses the power that is 
exerted. Hence the term '' power " means, not the energy expended, 
but the rate at which the energy is expended, twice as much power 
being developed where 100 foot-lbs. of work are done in 1 minute 
as in the case where 100 foot-lbs. are done in 2 minutes. 

Mechanical power is always expressed as so much horse-power, 
this term having come into use in the early days of the steam-engine, 
when engines were made chiefly to take the place of horses. It was 
then estimated that the horse was capable, on average working, of 
doing 33,000 foot-lbs. of work in 1 minute. This rate of doing 
work, namely, 33,000 foot-lbs. of work per minute, or, what is the 
same thing, 550 foot-lbs. per second, is accepted as the standard, the 
power so exerted being expressed as 1 horse-power, generally written 
1 H.P. 

Thus, if 33,000 foot-lbs. of work are done in 1 minute, work is 
done at the rate of 1 H.P. 

If 66,000 foot-lbs. of work are done in 1 minute, work is done at 
the rate of 2 H.P. 

If 66,000 foot-lbs. of work are done in 4 minutes, work is done 
at the rate of one quarter the above rate, namely, at the rate of 
i H.P. 

The above estimate of doing work is, no doubt, a high one, but 
this is of no practical consequence, as the power of engines, motors, 
etc., is now always calculated, not from the number of horses that 
might have to be replaced, but from the number of foot-lbs. of work 
that have actually to be done in a given time. Thus, the figure 
33,000 can be looked upon as simply a number which, when divided 
into the number of foot-lbs. of work done in 1 minute, gives a 
number expressing the horse-power. 

Before leaving this subject, it may be pointed out that a horse 
can and may exert a great deal more than 1 H.P. for a short 
space of time, the figure 33,000 being assumed to be an average, 
say, for a day's work. Thus, to replace a horse which is capable of 
pulling a car with a motor which is capable of giving out as a 
maximum 1 H.P. would not be altogether a fair substitution, the 
motor being rated at its maximum, and the horse at its average. 

While a motor can temporarily sustain a considerable overload, 
it may be said that the horse-power of motors for traction work, as 



70 ELEMENTS OF ELECTRIC TRACTION 

generally given, is that maximum power which they are capable of 
exerting continuously with a given temperature rise — 75° Fahr. above 
the surrounding atmosphere being the usual temperature rise. The 
heating up of the armature and field of a motor, due to the current 
it carries, is one of the factors that determines the load it can safely 
carry for any length of time. 

Before leaving the above portion of the subject, the reader should 
carefully note the distinction between the three different quantities, 
namely — 

1. Force simply expressed, say, as so many pounds. 

2. Total work done, or energy expended, expressed, say, as so 
many foot-lbs. 

3. Power or rate of doing work, expressed, say, as so many foot- 
lbs, of work done per minute, or as so much horse-power. 

As already seen, in an electric motor two forms of energy are 
dealt with, and consequently have to be measured, namely — 

1. The electrical energy supplied. 

2. The mechanical energy generated, or, more strictly speaking, 
transformed. 

Electrical Energy and Power. — No attempt will be made 
here to fully prove the following statements with regard to the 
measurement and calculation of electrical energy and power; the 
facts simply are stated, and an idea given as to the underlying 
reasons. The reader should again carefully note the distinction 
between electrical energy or work done, and the rate at which the 
work is done, or, in other w^ords, the electrical power. 

Now, in the simple case of a v^eight being lifted, just as the foot- 
lbs, of work done is obtained by multiplying the pounds weight lifted 
by the distance the weight is lifted in feet, so also in a similar 
manner the electrical work done, say, by a generator, is obtained by 
multiplying the coulombs quantity of electricity passing through the 
circuit by the difference in electrical level, as it were, or pressure 
that it has been raised through or to ; in other words, by the volts 
pressure generated. This, however, is not expressed as so many 
volt coulombs, but as so many joules — ^joule being a term used to 
represent a certain quantity of energy. 

Example. — If 10 couls. quantity of electricity pass through a 
circuit, across which there is a difference of pressure of 8 volts, 
10 X 8, namely 80 joules, of electrical work will have been expended, 
that amount of work or energy having been supplied by some form of 
generator. 

The term "joule " thus corresponds in general meaning to the term 
" foot-lb. ; " that is, it is a measure simply of work done, 1 joule being 
equivalent, roughly speaking, to about |- of a foot-lb., more accurately, 
0737 foot-lb. This term, however, is seldom employed in practical 



POWER AND POWER MEASUREMENT 71 

work, a much larger standard or unit of measurement — as will be 
explained later — being employed. 

Now, just as the pounds weight lifted in a given time multiplied by 
the height in feet it has been lifted is a measure of the rate at which 
work is being done, and hence the power supplied, work at the rate 
of 33,000 foot-lbs. per minute, or 550 foot-lbs. per second, being 
equivalent to 1 H.P., so also the number of coulombs per second 
that are raised to a given pressure, multiplied by the pressure in 
volts, is a measure of the rate at which electrical work is bein<? done. 
The coulombs per second, however, are equal to the current in 
amperes passing through the circuit. Hence, if the number 
expressing the amperes be multiplied by the number expressing 
the volts, a number will be obtained expressing the rate at which 
electrical energy is being expended, or, in other words, will express the 
value of the electrical power expended, namely, the number of joules 
per second, or, to use the general term, the number of watts. Work 
done at the rate of one joule per second is equivalent to an electrical 
power of 1 watt. The term "watt" thus corresponds to the term 
" horse-power " in general meaning ; that is, it is a rate of doing work. 

Now, since 1 watt is equal to 1 joule per second, and 1 joule 

is equivalent to 0'737 foot-lb., 1 joule per second is equivalent to 

work being done at the rate of 0"737 foot-lb. per second. To do 

work at the rate of 1 H.P., it must be done at the rate of 550 foot- 

550 
lbs. per second. Therefore, to do work at the rate of 1 H.P., ,^ ^- , 

namely, 746 joules of work, must be done per second ; in short, 746 
watts are equivalent to 1 H.P. Generally, this is expressed by 
saying 746 watts equal 1 E.H.P. (Electrical Horse Power). 

Example. — A dynamo giving out 10 amps, at a pressure of 74*6. 
volts will be giving out an electrical power of 10 x 74*6, namely, 
746 watts, and if all the electrical energy supplied at this rate could 
be converted by means, say, of a motor, into mechanical energy, the 
motor would be capable of doing work at the rate of 1 H.P. 

Thus, in 1 second 10 x 1, namely 10 couls., would pass through 
the circuit. 

10 X 74" 6 = 746 ; that is, 746 joules of electrical work will be 
done per second. 

746 X 0'737 = approximately 550 foot-lbs. of work done per 
second, and this is equal to work done at the rate of 1 H.P. 

As the amount of power represented by 1 watt is very small, a 
larger standard, termed a kilowatt, is employed, 1 kilowatt being 
equal to 1000 watts. 

In charging for electrical supply, the total energy supplied is 
required, and not simply the rate at which the consumer may use it. 

Now, as the amount of electrical energy represented by 1 joule 



72 ELEMENTS OF ELECTRIC TRACTION 

is very small, a larger standard of measurement has been adopted by 
the Board of Trade, which is called the Board of Trade unit. Thus 
the Board of Trade unit is a measure, not of the power supplied to a 
circuit, but of the total electrical energy ; in fact, it corresponds simply 
to a given number of foot-lbs. The energy represented by the Board 
of Trade unit is generally expressed as being equivalent to 1000 watt 
hours. That is, if 1000 watts are continuously supplied to a circuit 
for one hour, a certain amount of energy will have been expended, 
and that energy will be equivalent to one Board of Trade unit. 

Thus, again, if 250 watts are supplied to a circuit for 4 hours, 
one Board of Trade unit will have been supplied, or if one watt is 
supplied to a circuit for 1000 hours, one Board of Trade unit will have 
been supplied, the total energy in each case being the same. 

While dealing with these practical standards of measurement it 
may also be said that the quantity of electricity represented by one 
coulomb is also very small, and in practical work a larger quantity 
is generally taken as a standard. The standard taken is that 
quantity of electricity that would pass through a circuit if one 
ampere flowed for one hour, this is equal to 3600 couls., and is 
termed an ampere hour. 

Summing up, the above results can be stated in the following 
manner : — 

Amperes X volts = watts 

1000 watts = 1 kilowatt 

746 watts = 1 E.H.P. 

Watts multiplied by the hours'^ , , , 

,, j.1. V J Y = watt hours 

the watts are supplied j 

Watt hours divided by 1000 = Board of Trade (B.O.T.) units 

Amperes multiplied by the hours) ^ ^^ ^^^^^^ 

the current is liowmg J ^ 

Therefore, to actually measure the electrical power supplied, say 
to a motor, all that need be done is to insert an ammeter in the 
circuit to measure the current, and to place a voltmeter across the 
motor terminals to measure the pressure of supply. 

From these two quantities, as seen above, either the watts or 
E.H.P. supplied can be calculated. Another plan would be to insert 
a wattmeter in circuit, an instrument which measures direct the 
watts supplied. 

Efficiency. — As already mentioned, energy is always lost as far 
as useful purposes are concerned, either in the transmission or trans- 
formation of energy. In consequence of this, the power obtained 
from an electric motor is always less than the power supplied, a 
certain amount of energy being absorbed in overcoming friction, and 
in various other ways, which will be detailed later on. 



POWER AND POWER MEASUREMENT 73 

Consequently, while the electrical power supplied either in watts 
or in E.H.P. can be easily measured and calculated as indicated 
above, to obtain the actual H.P. available, either the H.P. lost will 
have to be measured, and in this way the H.P. available calculated 
by deducting the power lost from the power put in, or else the H.P. 
available for use will itself have to be measured. This latter is the 
plan generally adopted. 

The actual H.P. a motor is capable of giving out is termed the 
Brake Horse Power, generally written B.H.P. 

The term B.H.P. arose from the method adopted of measuring the 
available H.P. that an engine or motor was capable of giving out, 
this being done by means of a brake applied to the rim of a pulley 
fixed to the motor or engine shaft as the case might be. This was 
expressed as the H.P. measured on the brake, or simply the B.H.P. 

From this it will be seen that the term Electrical Horse Power 
(E.H.P.) is simply the equivalent of so many watts, and in the case 
of a motor may simply refer to the electrical power supplied, whereas 
the term B.H.P. always refers to the nett power available for use. 
It must be noted, however, that a given H.P., whether electrical or 
brake, refers to a definite amount of work done in a given time. 

The ratio of B.H.P. output to E.H.P. input is a measure of the 
efficiency. The efficiency thus simply stating what proportion of the 
power supplied is available for use. 

Efficiency is always given as a percentage, that is per hundred. 
Thus if a motor at a given load has an efficiency of 80 per cent. 
(80%), it means that for every 80 H.P. obtained for use, 100 H.P. has 
had to be supplied, or, to be more correct, there is this particular 
ratio of -^q between H.P. output and H.P. input, as it must by no 
means be inferred that a motor working at an efficiency of 80% 
necessarily gives out just simply 80 H.P. ; the efficiency simply 
expresses a ratio as stated, and that for the given load. 

Thus, with this particular efficiency -^Wr-fv-^— ^ - = tt^t 
^ "^ E.H.P. mput 1^^ 

For example, a motor giving out only 4 B.H.P., might have an 
efficiency of 80% when so working, in which case as ^^q or i expresses 

the ratio of . ^ , , 5 H.P. will be the E.H.P. supplied, 
input ^^ 

With this particular efficiency of 80% 

Input X i^on = output, or 

Output X ^^^~ = input, 

and in a similar way other efficiencies are calculated. 

Also if the H.P. output be divided by the H.P. input, and the 
result multiplied by 100, the number obtained will represent the 
efficiency per cent. 



74 



ELEMENTS OF ELECTRIC TRACTION 



The efficiency of a motor will depend both upon the design and 
construction. It must not, however, be inferred from above that the 
efficiency of a motor is a constant quantity ; as a matter of fact, the 
efficiency will vary with the load, the efficiency at light loads being 
less than the efficiency at loads approaching the full load of the 
motor. Not that the energy lost at light loads is greater than the 
energy lost at heavy loads, but that the energy lost forms a large 
proportion of the total energy expended. 

Brake Horse Power Measurement. — In order to determine 
the B.H.P. of a motor, it will be seen that if the number of foot-lbs. of 

work actually done in a given time can 

<-^.^^^ be measured, the H.P. output will simply 

^ ^* 'Y' " * ^ /X be a matter of calculation, knowing that 

^ \ ^^ 33,000 foot-lbs. of work done per minute 

f ^-K \ is equivalent to 1 H.P. The principle 

' / -^ N » Qf ^}je method generally adopted for 

measuring the work done in a given time 
is as follows : — 

Let two weights be attached to the 
ends of a belt laid over a pulley fixed 
to the motor shaft, as shown in Fig. 19. 
If these weights are equal, say, for ex- 
ample, 10 lbs. each, no motion of the belt 
will take place when the motor is at 
rest. If, however, the motor begins to 
rotate in the direction shown, owing to 
the friction between the belt and the 
pulley, the belt will be carried round 
lifting weight A, and lowering weight B. 
If, now, additional weights be added to A, 
until the belt just slips, so that weight A 
is neither lifted nor lowered, a state of balance will be brought about. 
Assuming in the above case that 5 lbs. have had to be added on to 
A to bring such a state of balance about, with the motor rotating at 
a given number of revolutions, then if the forces acting on the belt 
be considered, it will be seen that while there are 15 lbs. acting at A 
tending to pull that side of the belt down, there are only 10 lbs. 
acting at B, tending to pull it up, and since A does not move 
either up or down, the pull due to friction between the belt and 
pulley must account for the 5 lbs. difference. In short, the difference 
between the two weights is a measure of the pull that the motor is 
exerting under these conditions. In this way the pounds pull that the 
motor is actually exerting at the rim of the pulley can be measured. 
If, instead of a frictional resisting force of 5 lbs., an actual resisting 
force of 5 lbs. had been applied to the rim of the pulley, as would 




Fig. 19. 



POWER AND POWER MEASUREMENT 75 

have been the case had one end of the belt simply been fixed to the- 
pulley, and a weight of 5 lbs. attached to the other free end of the 
belt, the work done in a given time would have been just the same, 
the speed and pull in each case being the same. 

It will, however, be more readily seen from this latter case that 
the motion of the pulley would cause the weight of 5 lbs. to be lifted 
a distance equal to the circumference of the pulley in one revolution. 
(The circumference can be calculated by multiplying the diameter by 
3 14:, or 3|, or it can be actually measured by passing a tape measure 
round the pulley.) 

Knowing, then, the distance the pull is exerted in one revolution, 
if this be multiplied by the number of revolutions per minute, the 
total distance the pull is exerted in one minute can be calculated. 

This method of calculating the distance the pull is exerted 
applies in exactly a similar way to the case first considered, the 
substitution of one form of resisting force for another making no 
difference to the work done, the above explanation being added to 
make the reasoning somewhat simpler. 

From this it will be seen that if the effective pull, in the above 
example 5 lbs., be multiplied by the distance in feet moved through 
in 1 minute — this being calculated as indicated above — the foot-lbs. 
of work done in 1 minute will be obtained, and this, divided by 
33,000, will give the B.H.P. output. 

Actual Test of a Series Motor.~The following results were 
obtained from a small series motor tested in the above manner, with 
the exception that a spring balance took the place of the smaller 
weight : — 

Results obtained — 

Large weight at one side of belt, 37^ lbs. Spring-balance 
reading, 17 lbs. 

Revolutions per minute, 1210. 

Diameter of pulley = 4 inches, circumference = 12J inches, or 
1*04 feet, roughly speaking = 1 foot. 

Amperes passing through the motor = 10*2. 

Volts across terminals = 91*75. 

Calculation of B.H.P under above conditions — 

Effective pull == 37.} lbs - 17 lbs., namely, 20} lbs. 

Circumference of pulley = 1*04 feet, roughly speaking, 1 foot. 

Distance pull is exerted through in 1 minute = roughly, 
1 foot X 1210 = 1210 feet per minute. 
Foot-lbs. of work done per minute = 20} x 1210 = 24,805 foot- 
lbs. 

B.H.P = |M^ = roughly, 075 or | B.H.P. 
More accurate calculations show it to be 0*83 B.H.P. 



76 ELEMENTS OF ELECTRIC TRACTION 

That is, under above conditions of load, the motor was doing work 

at the rate of 0-83 B.H.P. 
Calculation of Efficiency — 

Watts input = 10'2 x 9175 = 935-8 watts 
E.H.P input = ?^ = 1-25 E.H.P. 

Efficiency per cent. = -— - X — — = 66'4 per cent, efficiency 

The above series motor is only a small one, and consequently its 
efficiency is not high compared with what would be obtained under 
similar conditions of test, say from a traction motor, which would 
have probably an efficiency at three-quarters full load of 80 per cent. 

Torque. — In traction work especially it is essential to know not 



-2-FEE7 




Fig. 20. 

only the power but also the force a motor may be capable of exerting. 
As, for instance, it may be desirable to know the force a motor exerts 
with a given current passing through it. 

The nature of the force exerted by the armature of a motor is such 
that it tends to twist the shaft round to which it is fixed. A force so 
acting is said to exert a certain twisting moment, or simply a certain 
torque* this term being derived from a Latin word meaning "to 
twist." 

Now, if two bars be fixed on to a shaft free to rotate as shown in 
Fig. 20, experiments will show that if a 1 lb. weight be suspended 
at a distance of 1 foot from the centre of the shaft, at one side, as 
shown, a certain twisting effect will be produced, and that this 
particular twisting effect can be balanced in a variety of ways. In 

* Pronounced " tork." 



POWER AND POWER MEASUREMENT 



11 



fact, it can be balanced by means of a force of any value one may 
choose, provided the force acts at a suitable leverage. Thus, for 
example, experiments will show that the twisting effect can be 
balanced, and in this way its equivalent in value be found, by 
suspending a 1-lb. weight at a distance of 1 foot from the centre, at 
the other side of the shaft, or by suspending in a similar way ; for 
instance — 



a ^-Ib. weight at a distance of 2 feet, as shown in the figure, 

,, „ ,, 4 leet, 
a jL-lb. „ „ „ 10 feet, 
,, a 4t-iD. ,, ,, ,, 



or a J-lb 



\ foot, and so on. 



The twisting effect or torque in each of the above cases is exactly 
the same. That is, for example, a ^-Ib. weight acting at a leverage 
of 4 feet produces exactly the same twisting effect as a 1-lb. weight 
acting at a leverage of 1 foot, or a xo4b. weight acting at a leverage 
of 10 feet, and so on. 




Fig. 21. 



Thus the twisting effect depends, not only on the weight or the 
force, but also upon the leverage at which it acts. 

The value of the torque is obtained, in all such simple cases 
where the force acts at right angles to the lever, by multiplying the 
force by the length of the lever. If the force is expressed in pounds, 
and the leverage in feet, the number obtained by so multiplying 



78 ELEMENTS OF ELECTRIC TRACTION 

will express the number of Ihs.-feet torque — this wording being 
purposely adopted to avoid confusion with foot-lbs, of work. 

In each of the above cases the torque is seen to be 1 Ib.-foot, and 
for a force to exert a 1 Ib.-foot torque, it simply means that what- 
ever be the value of the force, the leverage at which it acts is such 
that it produces exactly the same twisting effect as is produced by a 
force of 1 lb. acting at a leverage of 1 foot. 

Again, if a force of 10 lbs. acts at right angles to a lever fixed to 
a shaft, as shown in Fig. 21, and at a distance of 5 feet from the 
centre of the shaft, a torque of 10 X 5, namely, 50 lbs. -feet, will be 
exerted on the shaft, tending to twist the shaft in the opposite 
direction to the hands of a watch. 

Further experiments now will show that not only can this be 
balanced by a single torque of 50 lbs. -feet, brought about in any 
desired manner, as already indicated, acting in the opposite direction, 
but also that it can be balanced by a number of smaller torques, also 
brought about in any desired manner — as, for example, those shown 
in the figure all acting in the opposite direction, but such that their 
sum is equal to 50 Ibs.-feet torque. 

Thus, 5 X 5 = 25 Ibs.-feet torque. 

O X o ^^ J-0 ,, ,, 

10 X 1 = 10 „ 

Total 50 Ibs.-feet torque acting in a clockwise direction. 

It will now be seen that the above three torques are equal in 
value to a single torque of 50 Ibs.-feet. That is, these three will 
produce the same twisting effect as the one, provided, of course, they 
are arranged to act in the same direction as the one. 

Thus, a torque of 50 Ibs.-feet produced by a 10-lb. force acting at 
a leverage of 5 feet, could be replaced, for example, by five forces 
each of 1 lb. acting each at a leverage of 10 feet. 

It follows from this that a force, for instance, of 6 lbs., acting at 
a leverage of 3 feet, or its equivalent of 18 lbs. at 1 foot, produces 
nine times the twisting effect that a force of 2 lbs. does acting at a 
leverage of 1 foot ; the torque of the one being 18 Ibs.-feet, and that 
of the other 2 Ibs.-feet. 

The torque in any given case, it may be said, can also be ex- 
pressed in any other way desired, such as so many Ibs.-inches, or 
so many tons-feet, a torque of 50 Ibs.-feet being equivalent to one 
of 600 Ibs.-inches. 

Coming now to the case of a motor, if the sum of all the forces 
acting on the conductors be known, and the distance of the conductors 
from the centre of the shaft also be known — all conductors having the 
same leverage — the torque can be calculated by multiplying the value 



POWER AND POWER MEASUREMENT 79 

of the one by the value of the other. This, however, will not give the 
actual torque available, as a certain torque will be required to over- 
come friction and various other resisting torques. 

The torque of a motor is generally obtained either directly or 
indirectly from actual test, the result then giving the actual torque 
available. 

The available torque can be readily calculated if the particulars 
are to hand which were obtained on testing the B.H.P. Thus, 
referring to the test on the small series motor previously mentioned — 

The effective force when 10 '2 amps, were passing through the 
motor was seen to be 20 J lbs. 

The radius of the pulley was 2 inches, that is, I foot. 

Therefore the actual available torque when 10"2 amps, were 
passing through the motor was 20^ X ^ = 3"41 Ibs.-feet, or 41 Ibs.- 
inches. 

More accurate calculation — the real leverage, owing to the 
thickness of the belt, being slightly more than 2 inches — gives the 
torque as 3 '6 Ibs.-feet. 

The torque can also be calculated from the B.H.P. if the speed 
at which the motor runs when giving out this particular B.H.P. be 
known, this merely being a modification of the above calculation. 

Thus, if the B.H.P. be multiplied by the number 5252, and 
divided by the number of revolutions per minute, the resulting 
number will represent the Ibs.-feet torque the motor actually exerts 
when working under these particular conditions of B.H.P. and speed. 

Such statements as this are generally written in the following 

manner : — 

B.H.P. X 5252 , . IK r , 

— -. .— = torque m Ibs.-ieet. 

revolutions per minute 

The torque exerted by any given motor will primarily depend, as 
will be seen from what has already been said, upon — 

(1) The intensity of the field ; that is, upon the number of lines, 
say, per square inch ; 

(2) Upon the armature current ; 

as both the number and length of the conductors, also their leverage, 
will always be constant in any given motor. 

In the case of an ordinary series motor, the torque will simply 
depend upon the current passing through the armature, as the same 
current passes through the field, in this way determining the strength 
of the field. The torque in this way does not depend upon the 
speed ; consequently, with a given current and a given field strength, 
the torque exerted will be approximately the same whether the 
armature is at rest or in motion. Strictly speaking, this will not be 
quite true, as certain resisting forces are set up when the armature 
is in motion which do not exist when the armature is at rest, and 



8o 



ELEMENTS OF ELECTRIC TRACTION 



these forces will somewhat reduce the effective torque. It must, 
however, be borne in mind that to keep the current within reasonable 
limits when the armature is at rest, a certain amount of resistance 
will have to be inserted in circuit, or the voltage reduced, as under 
these conditions no back E.M.F. will be generated. 

The torque of a motor can in this way be measured when the 
armature is quite stationary ; all that need be done is to fix a lever on 
the shaft or pulley of the motor, as shown in Fig. 22, and attach one 
end of a spring balance to one end of the lever, the other end of the 




LEy£Rfl<(i£ WHEN Mm tS HORIlONTnL 



jQi 



Fig. 22. 



spring balance being suitably fixed. The pull then registered on 
the spring balance in pounds, multiplied by the leverage in feet, 
will give the torque in so many lbs. -feet that the motor exerts 
under any particular conditions of armature current and field 
strength. 

This method of measuring the torque, it may be said, introduces 
certain difficulties on account of friction, but by taking the average 
of two readings, one with the armature pulling the spring into a 
balancing position, and the other with the spring pulling the armature 
into a balancing position, these difficulties can be to a large extent 
overcome. 

The experiment is, however, merely described to illustrate the fact 
that the torque of a motor does not depend upon the speed, but simply 
upon the value of the current passing through the armature, and upon 
the strength of field. 

The action of a motor, as far as its torque and rotation is simply 



POWER AND POWER MEASUREMENT 



8i 



concerned, will now be looked at from a magnetic point of view. In 
Eig. 23, NS represents the field magnets of a 2-pole motor. If the 
brushes are connected by means of the commutator to the top and 
bottom conductors, current will circulate, as shown diagrammatically 
in the figure, round the armature core, passing down one side of the 




MOTOR 



Fig. 23. 



vertical centre line and up the other. Current so circulating will 
cause the armature core to become magnetized in a vertical direction. 
If, now, it be assumed that current is circulating in this particular 
case down the conductors, on the right-hand side of the vertical 
centre line, and up the conductor on the left, the armature core will 
become so magnetized that the top portion becomes magnetized 
with north polarity, and the bottom with south. The action, then, of 
the north and south poles of the field magnets on the north and south 
poles of the armature, will set up a twisting action on the armature, 
which will cause the armature to rotate if the load be a suitable one — 
that is, if the torque exerted by the armature is greater than the 
resisting torque set up by the load. 

The direction of rotation, looked at from a magnetic point of 
view^, will be found to agree with that when looked at from an 

G 



82 ELEMENTS OF ELECTRIC TRACTION 

electrical point of view, as can be tested by means of the left- 
hand rule. 

Thus the torque in any given motor will simply depend upon the 
strength of these magnetic poles ; that is, as already stated, upon the 
strength of field and upon the current fliowing through the armature, 
as the strength of the magnetic poles of the armature core depends 
upon the value of the armature current. 



Examples 

(1) A motor, on being tested under certain conditions, is found to 
do 27,500 foot-lbs. of work every 2 seconds. 

What B.H.P. is the motor exerting under these conditions ? 

Work is being done at the rate of ^^§~, namely, 13,750 foot- 
lbs, per second. 

As work done at the rate of 33,000 foot-lbs. per minute, or 550 
foot-lbs. per second, = 1 H.P. 

.-. B.H.P. = mi^ = 25 

Therefore, under above conditions, the motor is exerting 25 B.H.P. 

(2) If 50 amps, are supplied to a tramcar at a pressure of 500 
volts — 

(a) What is the value of the electrical power supplied, in watts ? 

(b) What is the E.H.P. supplied ? 

(c) If the motors have an efficiency of 75 per cent., including gear 
losses, what is the B.H.P. available for tractive purposes ? 

(a) . As watts = CE .*. watts = 50 x 500 = 25,000 watts. 

Therefore electrical power is being supplied of the value of 25,000 
watts, or simply 25 kilowatts. 

(h) As 746 watts = 1 E.H.P. 

.-. E.H.P. supplied = ^?f gi^ = 33-5 E.H.P. 

Therefore the value of the E.H.P. supplied = 33-5 E.H.P, 

(c) With an efficiency of 75 per cent. — 

B.H.P. = 33-5 X -1% = 251 B.H.P. 

Therefore the value of the power available for tractive purposes 
= 25 B.H.P. 

(3) Twenty amps, are supplied to a car at a pressure of 500 volts 
for 15 minutes, during which time the car travels IJ miles. 



POWER AND POWER MEASUREMENT 83 

(a) What number of B.O.T. units are supplied during that time ? 

(b) What would be the number of units taken by the car per 
mile? 

(a) . As watts = CE /. watts = 500 X 20 = 10,000 watts 
As energy is supplied at this rate for 15 minutes, or ^ hour, 
.*. energy supplied during the 15 minutes = l-S^ilil X i = 
2500 watt hours. 

As 1000 watt hours = 1 B.O.T. unit 
.*. energy is supplied of the value xooq, namely, 2*5 B.O.T. units. 

Therefore energy supplied during the 15 minutes is of the value of 
2-5 B.O.T. units. 

(b) As miles travelled = IJ 

25 
.". B.OT. units per mile = :pp = 1'66 

Therefore the car, under above conditions, would be taking energy 
at the rate of 1*66 B.O.T. units per mile, or this could be expressed 
as 1*66 B.O.T. units per car mile. 

(4) A motor exerts 24 B.H.P. when running under certain con- 
ditions at 800 revolutions per minute. 

(a) How many foot-lbs. of work will the motor do if it runs for 
1 hour ? 

(b) If the motor has an efficiency of 80 per cent., how many 
foot-lbs. of work done in this particular case will correspond to 
1 B.O.T. unit ? 

(a) Foot-lbs. of work done per minute = 33,000 X 24 = 792,000 
.-. foot-lbs. of work done in 1 hour = 792,000 X 60 = 47,520,000 

Therefore the work done in 1 hour is equal to 47,520,000 foot-lbs. 

(5) With an efficiency of 80 per cent., the E.H.P. supplied to the 

motor = 24 X -igHf = ^fg- = 30 E.H.P. 
30 E.H.P. = 30 X 746 watts = 22,380 watts 
22,380 watts supplied for 1 hour = 22,380 watt hours 
22,380 watt hours = \%%^- = 22-380 B.O.T. units 

Therefore in this case 22*380 B.O.T. units will correspond to 
47,520,000 foot-lbs. of work; 

Therefore 1 B.O.T. unit will correspond to ' ,^' ■' namely, 

2,123,324 foot-lbs. 

Therefore 1 B.O.T. unit will correspond in the above motor with 
an efficiency of 80 per cent, to 2,123,324 foot-lbs. of work done. 

(5) On a double route 3 miles long (length of complete journey 
6 miles) 12 cars are employed^ maintaining a 5 minutes' service, the 



84 ELEMENTS OF ELECTRIC TRACTION 

average speed of each car being 6 miles per hour. During a period 
of 12 hours, half the cars make 12 complete journeys, and the other 
half llj complete journeys, and the average power supplied is 100 
kilowatts. 

(a) What number of B.O.T. units would be supplied during the 
period of 12 hours ? 

(b) What is the total number of car miles run ? 

(c) What number of B.O.T. units are consumed per car mile ? 

(a) . . Average power supplied = 100 kilowatts 

= 100,000 watts 
/. energy supplied during the 12 hours = 100,000 x 12 

= 1,200,000 watt hours 
/.B.O.T. units suppHed during 12 hours = ^^i^o^o" = 1200 

Therefore the total electrical energy supplied during the 12 hours 
is equivalent to 1200 B.O.T. units. 

(b) Length of one complete journey = 6 miles 

Length of 12 complete journeys = 6 X 12, namely, 72 miles 

Total miles run by the 6 cars = 72 X 6 „ 432 „ 

Length of llj complete journeys = 6x11^ „ 69 „ 

Total miles run by the remaining 6 cars = 69 X 6 „ 414 „ 

Total miles run by the 12 cars = 414 + 432 = 846 miles 

Therefore total number of car miles run during the 12 hours 
^ 846 miles. 

(c) Total B.O.T. units supplied during the 12 hours = 1200 

Total car miles run during the 12 hours = 846 
.*. B.O.T. units consumed per car mile = ^g^W" ~ 1*418 

Therefore each car will require electrical energy of the average 
value 1*418 units for each mile the car runs. 

(6) The armature resistance (from brush to brush) of a series 
motor is 0*36 ohm, and the resistance of the series winding is 
0-76 ohm. 

(a) What will be the watts lost in heating up the armature when 
a current of 50 amps, passes through the motor ? 

(b) What will be the watts lost in heating up the field winding 
under the same conditions ? 

(a) As E = CE, a pressure of 50 x 0*36, namely, 18 volts, will 
be required to drive the 50 amps, through the armature itself. 
As CE = watts, .*. the watts lost in overcoming armature resist- 
ance = 50 X 18 = 900 watts. 



POWER AND POWER MEASUREMENT 85 

The watts lost could also be calculated as follows : — 

As CE = C^E, .-. watts lost = 50 X 50 x 0-36 = 900 watts as 
before. 
Therefore the electrical power expended in overcoming armature 
resistance = 900 watts. 

(h) . . , As C^R = watts expended 

.*. watts expended = 50 X 50 X 076 = 1900 watts 

Therefore the electrical power expended in overcoming the resist- 
ance of the field winding =: 1900 watts. 

The electrical energy expended in any given time in each of the 
above cases becomes converted into heat. 

(7) A motor exerts 24 B.H.P. at the armature shaft when running 
at 640 revolutions per minute. 

What is the effective torque exerted by the motor at the armature 
shaft ? 

. , . 11. 4. . B.H.P. X 5252 

As torque m Ibs.-reet = 



revs, per minute 

^ . ,, . , 24 X 5252 3 x 5252 15,756 

Torque m lbs. -feet = -—p: — = ^-r — = ' 

^ 640 80 80 

= 196-9 Ibs.-feet 

Therefore the torque exerted by the motor under the above con- 
ditions equals approximately 197 Ibs.-feet. 

(8) In the above example, what force would the motor exert at 
the rim of a pulley — 

(a) 30 inches diameter ? 
(h) 33 inches diameter ? 

(a) . 30 inches diameter = 15 inches radius = IJ feet radius 

As torque in Ibs.-feet = lbs. force x leverage in feet (or length 

of lever it is acting at right angles to in feet), 

„ n torque in Ibs.-feet 197 ,^, . , 

/. lbs. pull = -~^ . .. ^ = — p = 1^1 X 4 = 18^ = 157*6 lbs. 

^ leverage m feet IJ 1^0 5 xo<uiuo. 

Therefore pounds force exerted at the rim of a pulley 30 inches 
diameter = 157*6 lbs. 

(h) 33 inches diameter = 16J inches radius = ^^ X ^^ = || 

= 1*37 feet radius 

197 
.'. lbs. pull m this case = -— = 143*06, say 143 lbs. 

Therefore pounds force exerted at the rim of a pulley 33 inches 
diameter = 143 lbs. 



86 ELEMENTS OF ELECTRIC TRACTION 

(9) A 200-volt continuous-current motor is capable of exerting 
20 B.H.P. on full load, assuming an efficiency of 70 per cent. 

(a) What current will it take on full load ? 

(b) What number of square inches area should the cable have 
supplying the motor, if the density is not to exceed 750 amps, per 
square inch ? 

(c) What number of strands should the cable have if composed 
of wires of No. 15 gauge ? A 15-gauge wire has 0'004 square inch 
area. 

(a) With an efficiency of 70 per cent., 

E.H.P. input = 20 X -if^f = 28-5 
As 746 watts = 1 E.H.P. 
/. 28-5 E.H.P. = 28-5 X 746 = 21,261 watts 

As CE = watts /. C = ^ 

/. current = ^^§-'' = 106*3 amps. 

Therefore current taken by the above motor on full load = 106*3 
amps. 

(b) As current is not to exceed 750 amps, per square inch 

/. square inches area x 750 = 106*3 

/.square inches area = = 0141 

Therefore the cable, to fulfil the above requirements, must have an 
area of 0*141 square inch. 

(c) As a No. 15-gauge wire has an area of 0*004 square inch 

.*. no. of strands required of this gauge = ^ = 35*2 

As cables are usually made up in strands of 3, 7, 19, 37, 61, 
and so on, a cable of 37 strands would be suitable. 

Therefore the size of cable that could be employed could consist 
of 37 strands of 15 gauge, or simply a 37/15 cable. 



CHAPTER VII 
MECHANICS OF TRACTION 

It is essential, before dealing with the actual application of electric 
motors — or, as a matter of fact, any form of motive power to traction 
work — that both the nature and amount of the work to be done 
should be understood. 

For this purpose certain principles of mechanics, dealing with 
the motion of moving bodies as applicable to traction work, will be 
briefly explained. An application of these principles, together with 
certain experimental facts, will enable the pull and H.P. that a car 
will require when running under any given conditions of load, speed, 
or track to be estimated. In this way the size of motors for any 
given requirements can be determined. 

Before dealing with the actual estimate of the forces required in 
connection with the motion of a car, certain terms employed in 
dealing with motion must be clearly understood, and will, therefore, 
first of all be explained. 

Motion — Speed. — In dealing with the motion of a car, distinction 
first of all has to be made between distance travelled, irrespective 
of time, expressed simply, say, as so many miles, or so many yards 
or feet, and the distance travelled in a given time, expressed, say, as 
so many miles per hour, or so many feet per second. This latter 
expresses the rate or speed at which a car travels, taking time as it 
does into consideration. 

It must be clearly understood that when, for example, a car is 
said to be travelling at the rate of 15 miles an hour, there is nothing 
here to imply that the car has actually travelled or will travel a 
distance of 15 miles in one hour ; it may or it may not. All 
that is implied by such an expression is that the car is actually 
travelling at some given instant at this particular rate of speed, and 
that if this particular speed were maintained for one hour, then the 
car would, during that hour, travel a distance of 15 miles. Conse- 
quently, it will be seen that a car might only travel a few yards at a 
particular speed, as, for instance, will be the case when the speed is 
continually varying. 



88 ELEMENTS OF ELECTRIC TRACTION 

Therefore a car travelling at the rate of 15 miles an hour would 
travel at the rate of ^}^^ of the above distance in -^^f^ of the time, 
namely, ^§, or ^J of a mile, that is, 440 yards in one minute. 

Hence a speed of 440 yards per minute is equivalent to a speed 
of 15 miles per hour. In a similar way, a speed of 1 mile (5280 feet) 
per hour is equivalent to a speed of 88 feet per minute, and, roughly 
speaking, equivalent to a speed of 1 J feet per second, more accurately, 
1*46 feet per second. 

It will now be seen that if the distance, say, in yards, that a car 
travels be divided by the number of seconds taken to travel that 
number of yards, the result will give the speed at which the car is 
travelling during that time, expressed as so many yards per second. 

If the speed has not varied during the time under consideration, 
the speed calculated will be the actual speed at any given in- 
stant during that time. A car moving in this way would be said 
to be travelling at a uniform speed, moving, as it does, over equal 
distances in equal times. 

If, on the other hand, the speed has varied during the time 
considered, the speed obtained will be the average speed during that 
time, and not the actual at any given instant. 

It will be seen from this that the average speed may give no 
indication as to the actual speed at any given instant, as, for instance, 
in cases where the variations in speed are very great. 

Where the speed is varying, the actual speed at any given instant 
can be approximately obtained by taking the average speed during a 
short interval of time, during which the speed has not had time to 
vary much. Then the average speed during that short interval of 
time can be taken as approximately equal to the actual speed at any 
given instant during that time. 

Acceleration. — The next distinction that has to be made in 
dealing witli the motion of a car, when the speed is a variable one, 
is that between the speed at which a car is travelling, and the rate at 
which the speed is varying ; that is, the rate at which the speed is 
being increased or decreased, as the case may be. 

For example, if a car is travelling at a given instant at a speed 
of 4 miles per hour, and if it is also uniformly increasing its speed in 
such a way that 3 minutes later its speed is 7 miles per hour, then an 
increase of 3 miles per hour in the speed has taken place in 
8 minutes ; that is, its speed has increased at'the rate of 1 mile per 
hour every minute. 

Thus, at a given instant the speed was 4 miles per hour, 
1 minute later the speed was 5 „ „ 

1 minute later again the speed was 6 „ „ • 

1 7 

Then, in this particular case, 1 mile per hour per minute is said 



MECHANICS OF TRACTION 89 

to be the value of the acceleration, the term " acceleration " expressing 
the rate at which the speed increases. The acceleration is said to be 
uniform when equal increases of speed take place in equal intervals 
of time, as in the above case. 

Again, if a uniform acceleration of 1 J miles per hour per second 
— an acceleration sometimes adopted in traction work — were given 
to a car starting from rest, then — 

To start with, in this case, the car's speed would be — 0, 

1 second after starting, its speed would be 1^ miles per hour, 

2 seconds „ „ „ 3 „ „ 
o 41 

and 12 seconds would be required for the car to get up a speed of 
18 miles per hour. 

Had the car, instead, had an acceleration of 1 mile per hour per 
second, then 18 seconds would have been required for the car to get 
up the same speed of 18 miles per hour. 

Hence, the greater the acceleration, the greater will be the speed 
attained in any given time. 

In speaking thus of acceleration, the idea of time has to be 
employed twice, once in order to express the increase of speed that is 
taking place, and once again in order to express the length of time 
that would be required for this particular increase of speed to take 
place. 

When a car is slowing down, that is, its speed is being decraesed, 
the term " retardation " is used — the term " retardation " expressing 
the rate at which the speed of a car is being decreased, just as the 
term " acceleration " expresses the rate of increase. 

If the difference in speed, expressed, say, in so many miles per 
hour taking place in any given time, be divided by the time, say, in 
seconds, taken to bring about this difference of speed, the result will 
give the value of the acceleration or retardation during the time 
considered, expressed as so many miles per hour per second. 

If the acceleration has been a uniform one, the result obtained 
will give the actual acceleration at any instant during the time 
considered. 

If the acceleration has been a variable one, the result obtained 
will be the average acceleration during the time. The average 
acceleration may, however, give no indication as to the actual 
acceleration at any instant during the time considered if the variation 
has been great. 

It is useful to remember that an acceleration of 1 mile per hour 
per second is equivalent to, roughly speaking, an acceleration of 
1^ feet per second per second, more accurately, 1*46 feet per second 
per second. 



90 ELEMENTS OF ELECTRIC TRACTION 

This arises from the fact that a speed of 1 mile per hour is 
equivalent to a speed of 1'46 feet per second, roughly, 1^ feet per 
second, hence an increase in speed of 1 mile per hour is equivalent to 
an increase in speed of 1 J feet per second. 

Consequently, an acceleration of 1 mile per hour per second is 
equivalent to an acceleration of 1 J feet per second per second. 

In a similar way, an acceleration of 1^ miles per hour per second 
is equivalent to an acceleration of 2-2 feet per second per second, 
roughly, 2J feet per second per second. 

The reader should now carefully note the distinction between — 

(^a) Distance simply expressed, say, as so many miles. 

(h) Speed expressed, say, as so many miles per hour. 

(c) Acceleration expressed, say, as so many miles per hour per 
second. 

It may now be stated that the total force or pull required for 
traction purposes in any given case will be made up of forces required 
for the following purposes : — 

(1) Force required for accelerating purposes. 

(2) Force required to overcome the various resisting forces due 
to the resistance set up by friction. 

(3) Force required to balance the gravitational pull that exists 
when a car is on a gradient. 

(1) Accelerating Force. — Experiments and investigations in 
mechanics both show that, apart from friction and other external 
resisting forces, no force whatever is required simply to maintain a 
car at any speed which it has had given to it previously. In actual 
practice, of course, a pull has to be exerted to maintain a car at any 
given speed ; but the pull is simply that required to balance the 
resisting forces due to friction, and if on a gradient, to balance the 
downward pull due to gravitation. Now, while no force apart from 
those already mentioned is required to maintain a car at any given 
speed when once it has had that speed imparted to it, a force is 
required to change the speed of a car, and that apart from any force 
required for friction, etc. This is due to what is termed the inertia 
of the car ; in other words, it is an inherent property of matter that to 
set a quantity of matter in motion, or to change its speed, a force is 
required. 

It may here be said, a force is also required to change the direction 
of the motion of a body, but as this is not directly applicable to the 
question now being considered, it will not be dealt with. 

If experiments be made, say, for example, with a small experi- 
mental truck or car, it will be found that, if a definite force say 
of so many pounds be applied — that is, apart from the force which 
might be required to overcome friction, etc. — so as to move the 
truck in some given direction, under the action of such a force, not 



MECHANICS OF TRACTION 91 

only will the car begin to move and so gain speed, but also it will 
gain, and continue to gain speed at some uniform rate as long as 
this force is applied. In short, its acceleration will be constant, 
and experiments will still further show that if either the weight or 
the force be altered, the acceleration will be altered. 

Variable Force. — Thus it will be found with a given load — that is, 
total weight, including weight of truck — the greater the force applied, 
the greater will be the acceleration, and the less the force applied, 
the less will be the acceleration. If the force be kept constant, the 
acceleration will be kept constant, that is, with the given load. 

Variable Load. — On the other hand, with a given force applied 
to the truck, it will be found the greater the weight of matter that is 
being set in motion, the less will be the acceleration, and the less the 
weight, the greater will be the acceleration. If the weight be kept 
constant, the acceleration will be constant, that is, with the given 
force. 

Thus, if in any given case the force applied and total weight in 
motion are kept constant, the acceleration will be constant ; that is, 
the truck will continue to gain speed at some uniform rate, an increase 
or decrease in the force applied bringing about a corresponding 
increase or decrease in the acceleration. 

It should be noted that if the accelerating force in any given case 
be decreased,|the result will be, not a decreased speed, but a decreased 
acceleration; that is, the car will continue to gain speed, but at a 
lesser rate. 

More definite experiments show that a force of 1 lb. (friction, etc., 
being neglected) will give to a small truck weighing 32 lbs. an 
acceleration of 1 foot per second per second, and as long as this force 
of 1 lb. is applied, so long will the truck continue to increase its 
speed at the rate of 1 foot per second every second. 

To give an acceleration of twice this amount, namely, 2 feet per 
second per second to the 32 lbs., 2 lbs. would be required. 

To give an acceleration of 1^ times this amount, namely, 1 J feet 
per second per second to the 32 lbs,, 1^ lbs. would be required, 
and so on. 

On the other hand, while a force of 1 lb. will give an acceleration 
of 1 foot per second per second to a truck weighing 32 lbs., 

2 lbs. would be required to give the same acceleration to a truck 
weighing 64 lbs., 

1| lbs. to give the same acceleration to a truck weighing 48 lbs., 
and so on. 

If the car is being retarded, that is, if its speed is being reduced, 
the applied force will have to act in such a way as to oppose its existing 
motion. 

From this it will be seen that the rate at which the speed of a 



92 ELEMENTS OF ELECTRIC TRACTION 

car either increases or decreases, that is, the value of the acceleration 
or retardation, will depend upon two things — 

1. The total weight of matter the motion of which is involved. 

2. The accelerating or retarding force applied. 

Having now given that a force of 1 lb. is required to give an 
acceleration of 1 foot per second to a truck weighing 32 lbs., it will be 
seen that seventy times this force will be required to give the same 
acceleration to a truck weighing seventy times this amount. 

That is, 70 lbs. will be required to give an acceleration of 1 foot 
per second per second to a truck weighing seventy times 32 lbs., 
namely, 2240 lbs., that is, 1 ton. 

Now, since an acceleration of 1 mile per hour per second is 
equivalent to an acceleration of, roughly, 1|- feet per second per 
second, IJ times 70 lbs. will be required to give an acceleration of 
1 mile per hour per second to a truck weighing 1 ton. 

That is, 105 lbs., more accurately 102"6 lbs., will be required to 
give an acceleration of 1 mile per hour per second to a car weighing 
1 ton. 

For rough calculation, 100 lbs. per ton can be taken as the 
requisite force to give the above acceleration. 

In this way, from the above figures the force required to give a 
car of a given weight a given acceleration can be calculated. 

The force required can also be calculated in the following way, 
this simply being another modification of the above : — 

If the weight of the car in pounds be divided by thirty-two, and 
the resulting number multiplied by the value of the acceleration 
required in feet per second per second, the result will give a number 
expressing the value of the force required in pounds. 

Thus— 

Weisrht in pounds x ace. in feet per sec. per sec. 

^ —^ :z^ = force m pounds 

(2) Frictional Force. — In Fig. 24 is shown a simple piece of 
experimental apparatus consisting of a small truck, to which is 
attached a cord passing over a pulley, the free end of the cord having 
attached to it a scale-pan. 

By this means, varying forces can be applied to the truck so as 
to pull it along by placing weights in the scale-pan. 

If, now, a series of simple experiments be made with apparatus 
similar to that described, first of all with the wheels detached, the 
truck simply sliding along the table, it will be found that, with a given 
weight in the truck, a given force is required just to move the truck, 
and that any less force than this will fail to do so. This can be best 
done by gradually increasing the applied force until the truck just 
begins to move. 



MECHANICS OF TRACTION 



93 



The force required to move the truck is a measure of the resisting 
force set up by friction, and unless the friction is excessive, the force 
required to slide the truck will be found to be only a fractional part 
of the total weight. 

Experiments will also show that the force required will, roughly 
speaking, depend upon — 

(1) Total weight of truck and load. 

(2) The nature of the surfaces and degree of lubrication. 

Thus, the greater the weight, or the rougher and less lubricated 
the surfaces, the greater will be the pull required. 

This pull, it must be clearly understood, is simply that required 
just to overcome frictional resistance, and a pull over and above this 
will have to be applied to impart any given acceleration to the truck. 



o o 



K/'V— 





Fig. 24. 



It should, however, be stated that the friction that exists when 
the truck is at rest, that is, when it is just on the point of moving, 
is not the same as the friction that exists when the truck is in a 
state of motion. With dry surfaces the difference is, however, only 
small, the friction of rest being slightly greater than the friction of 
motion ; with lubricated surfaces the difference is greater, depending 
upon the nature of lubrication, etc. 

The ratio of the pull that has to be exerted in any given case to 
the total weight is termed the *' coefficient of friction " for the par- 
ticular surfaces in contact. 

Thus, if the truck and table are both of polished iron, and the 
surfaces are not lubricated, and it is experimentally found — total 



94 ELEMENTS OF ELECTRIC TRACTION 

weight of truck and load being 10 lbs. — that 2 lbs. are just re- 
quired to move the truck, then -^^ or J would be termed the '' co- 
efficient of friction " for polished iron to iron not lubricated. This 
ratio for these particular surfaces in their particular conditions will, 
roughly speaking, be found to be fairly constant for all reasonable 
loads that can be put upon them. Consequently, if the load were 
increased so that truck and load weighed 20 lbs., then 20 X J, 
namely, 4 lbs., would be required just to move the particular 
load. 

Now, if the pull in pounds that has to be exerted just to over- 
come the friction in any particular case be multiplied by the distance 
in feet the truck say is moved, the result will give the number of 
foot-lbs. of energy which have been expended in simply overcoming 
frictional resistance. 

This energy, it should also be added, will be transformed chiefly 
into heat energy, and is simply wasted, as far as all useful purposes 
are concerned. 

Thus, whenever surfaces slide or rub together, energy to a greater 
or less extent has to be expended in this way. 

If, now, wheels or rollers be attached to the truck, it will be 
found that the pull required for a given load is considerably less, the 
friction, being much reduced, the wheels now rolling and not sliding 
over the surface. It should, however, be noted that, were it not for 
friction, the wheels would simply slip, and motion of the truck would 
not take place. 

The friction, on the other hand, between the wheels and the rails 
does not bring about any loss of energy, as no sliding— unless the 
wheels slip — takes place. 

The energy expended, however, is that in rolling the wheels over 
the surface ; and investigations seem to indicate that the energy 
expended in rolling a wheel — that is, apart from slip and flange 
friction — is the outcome of the constant pressing of the wheel into 
the material of which the rails are composed. 

In actual traction work, the frictional resistance to traction, or 
tractive resistance, as it is termed, is due to — 

(1) Friction of axles in axle-boxes. 

(2) Friction of wheels rolling over the surface of the rails, includ- 
ing friction due to slipping of wheels and friction of the flanges 
against the side of the rails. 

(3) Friction due to the motion of the car through the air and to 
wind. 

The force required to pull a car along against all the resisting 
forces set up by friction due to the above causes is sometimes termed 
the " tractive effort." 

Various experiments have been made to actually determine the 



MECHANICS OF TRACTION 



95 



pull or tractive effort required under different conditions of track 
and speed. 

Some actual experiments made with tramcars running on grooved 
rails — the friction with grooved rails, it may be said, is about twice as 
great as that with ordinary rails as used in railway work — show that 
for clean rails on the level and straight, a tractive effort of 22 to 
25 lbs. for every ton weight (that is, car and passengers) is required 
to pull a car along when travelling at a uniform speed of some 6 or 7 
miles per hour. It must be noted, however, that the friction due to the 
resistance of the air increases rapidly with increase of speed, and in 
railway work, where much higher speeds are adopted than in ordinary 
tramway work, the friction due to this cause amounts to a serious 
item. In going round curves, or with dirty, clogged rails, more 




Fig. 25. 



friction is introduced, and a pull in such cases possibly of some 
50 lbs. or more per ton would be required ; 25 to 30 lbs. per ton 
weight can, however, be taken as a fair average tractive effort required 
to overcome frictional resistance in tramway work. 

Thus, with a 10-ton car, and a tractive resistance of 30 lbs. per 
ton, 300 lbs. pull would be required to overcome the resistance due 
to friction. 

(3) Gravitational Force. — In Fig. 25 is shown a slight modifi- 
cation of the apparatus described when dealing with friction, the truck 
being now placed on an incline, or gradient, as it is generally termed. 
It will be seen, on referring to this figure, that the truck in travelling 
from A to E is raised a vertical height equal to the distance BC. 

If AB were 12 feet, and the gradient such that BC was 3 feet, the 



96 ELEMENTS OF ELECTRIC TRACTION 

truck, it will be seen, rises 3 feet in travelling 12 feet ; that is, it 
would rise 1 foot in travelling 4 feet. This latter is the general 
method of expressing a gradient, and such a gradient would be 
spoken of as a gradient or grade of 1 in 4, sometimes written I. 

' Thus, a gradient expresses the number of feet a car travels in 
rising a vertical height of 1 foot. 

Gradients are also sometimes expressed as a percentage, the per- 
centage expressing the number of feet a car would rise vertically in 
travelling a distance of 100 feet. 

Thus, a gradient of 1 in 4 is the same as a gradient of 25 in 100, 
or simply a gradient of 25 per cent. In a similar way, a gradient of 
1 in 10 is a 10-per-cent. gradient. 

In mounting a gradient, then, work must be done apart from 
anything else in simply raising the car from one level to another. 

Thus, if a truck weighing 1 ton is moved up an incline of 1 in 10, 
the weight of 1 ton will be raised a height of 1 foot for every 10 feet 
the truck travels. Then the work done in simply raising the truck 
when it travels the distance of 10 feet will be 2240 lbs. x 1 foot, 
namely, 2240 foot.-lbs. 

Now, apart from friction, etc., the energy expended in foot-lbs. 
must equal the work done. 

That is, if 2240 foot-lbs. of work have been done, 2240 foot-lbs. 
must have been expended. Assuming the truck has been pulled up 
the gradient by means of an engine, then the pull in pounds exerted 
by the engine, multiplied by the 10 feet the distance the pull has 
been exerted through, must equal the 2240 foot-lbs. of work done 
in raising the truck. 

That is, a pull of 224 lbs., apart from friction, etc., must have 
been exerted. 

In calculating this pull, friction, etc., it must be remembered, has 
been ignored, and this pull of 224 lbs. is simply the pull that would 
be required if friction did not exist to balance the truck, and prevent 
it running down the incline due to gravitation. 

Consequently, to actually move a 1-ton truck up such an incline 
would require a greater force than 224 lbs., since force would be 
required, not only to overcome friction, but also to impart motion to 
the truck. 

If the truck were allowed to run down the incline, the force of 
224 lbs., less the force required for friction, would be available for 
accelerating the truck. 

From this the following rule is obtained for calculating the pull 
required to balance the downward pull of a car on a gradient : — 

Bide. — If the total weight of the car in pounds be divided by, say, 
the number of feet the car has to travel in order to rise a vertical 
height of 1 foot, the result will give the number of pounds pull that 



MECHANICS OF TRACTION 97 

will be required to balance gravitational effects, due to this particular 
weight of car and this particular gradient. 

The above can be experimentally shown by means of the appa- 
ratus illustrated. Thus, if the gradient is arranged to be 1 in 10, 
then if total weight of truck is 20 lbs., it will be found that, if the 
friction is negligible, 2 lbs. will be required to balance the tendency 
of the truck to run down the incline. 

If the truck weighs 30 lbs., 3 lbs. pull will be required. 

Further experiments will illustrate that the greater the weight, 
or the greater the gradient, the greater will be the pull required. 

As a practical application of the above, it will be seen that when 
a car is on a gradient of 1 in 100, the downward pull due to this 
gradient will be ^ym, namely, 22'4 lbs. per ton weight of car, and as 
this is about the force that will be required just to overcome friction, 
that is, with clean rails and on the straight, a car on a gradient of 
1 per cent, would, if the above figures are correct, just be on the 
point of running of its own accord down the incline. With any less 
incline, the car would not move of its own accord, and with any 
greater incline a force would be available for acceleration. 

Again, when a car is on a gradient of 1 in 2 2 '4 — roughly, 4^ per 

2240 
cent. — the downward pull due to this gradient will be , namely, 

100 lbs. per ton weight of car. As this is, roughly speaking, the 
force required to give an acceleration of 1 mile per hour per 
second, it will be seen that if friction be neglected, a car, on moving 
down such a gradient of its own accord, will have given to it an 
acceleration of 1 mile per hour per second. 

From this it will now be seen that a gradient of 4J per cent. 
+ 1 per cent., namely 5| per cent., will give a total gravitational 
pull of some 123 lbs. per ton weight, a pull sufficient to overcome 
friction and give an acceleration of about 1 mile per hour per second. 

In other words, a car on a gradient of 5^ per cent, will, on the 
above assumptions, attain a speed in descending the incline of its 
own accord of some 30 miles per hour in half a minute. 

It has now been shown how the various forces required for 
accelerating, overcoming frictional and gravitational effects can be 
estimated. An example will now be taken to illustrate the method 
of calculating not only the pull, but also the average H.P. and energy 
expended. 

Example. — Determine the total force that would be required to 
give a 10-ton car an acceleration of 1^ miles per hour per second on 
a gradient of 1 in 20. The tractive resistance being taken as 25 lbs. 
per ton. 

Force required for accelerating the car — 

As 102'6 lbs. per ton are required to give an acceleration of 

H 



^8 ELEMENTS OF ELECTRIC TRACTION 

1 mile per hour per second, 102-6 X IJ, namely, 153-9, say 154, lbs. 
per ton would be required. 

Therefore force required for accelerating = 154 x 10 = 1540 lbs. 

Force required for overcoming frictional resistances * — 

Tractive resistance taken as 25 lbs. per ton. 

Therefore force required to overcome friction = 25x10= 250 lbs. 

Force required to halance gravitational effects — 

On a gradient of 1 in 20, ^f *-^, that is, 112 lbs. per ton 
would be required. 

Therefore force required to balance gravitational 1 _ w^^ ^^^ 
effect = 112 X 10 J ' 

Total force required for all purposes = 2910 lbs. 

Morse-power. — With a uniform acceleration of 1^ miles per 
hour per second, at the end say of 10 seconds, the car will have 
attained a speed of 1^ x 10, namely 15 miles per hour. 

As 1 mile per hour is equivalent to a speed of 1*46 feet per 
second, 15 miles per hour is equivalent to a speed of 1'46 X 15, 
namely 21 '9, say 22 feet per second. 

Its average speed will then have been 11 feet per second, and in 
the 10 seconds the car will have travelled a distance of 11 x 10, 
namely 110 feet. 

Therefore foot-lbs. of work done in ) i c < a .. n n ^ac\ Af\f\ 
1 . . .1 \ = 1540 X 110 = 169,400 

accelerating the car ) ' 

Therefore foot-lbs. of work done iii)_ 250 x 110= 27500 
overcoming friction ) ~ ' 

Therefore foot-lbs. of work done in ) _ i -i on w i in _ 1 03 OQO 
overcoming gravitation f """ "" ' 

Total foot-lbs. of work done during the 10 seconds = 320,100 

It should be noted that the total work done during the 10 seconds 
could also have been calculated simply from the total pull ; thus — 

2910 X 110 = 320,100 foot-lbs. 

As the above amount of work has been done in 10 seconds, 
work will have been done at the average rate of -^J^--, namely, 
32,010 foot-lbs. of work per second. 

As work done at the rate of 550 foot-lbs. per second = 1 H.P., 

* The tractive resistance, with a given weight of car under given conditions, is less 
on a gradient than on the level, as the pressure normal to the surface is less. This 
difference with the gradients generally found is, however, so slight that it is here 
neglected. 



MECHANICS OF TRACTION 99 

work will have been done during the 10 seconds at the average 
rate of ^f gJH, namely, 58-2 H.P. 

Therefore total pull required to give a 10-ton car an acceleration 
of IJ miles per hour per second on a gradient of 1 in 20 = 2910 lbs. 

Average H.P. exerted during the 10 seconds = 58*2 H.P. 

The above, it must be particularly noted, is simply the average 
H.P. exerted during the 10 seconds as indicated. The actual H.P., 
for instance, exerted at the particular moment the car is travelling 
at the speed of 15 miles per hour will be just double the above, 
namely, 116*4 H.P., assuming, of course, that the pull of 2910 lbs. 
is still being exerted at this speed. The actual behaviour of a motor 
and the pull that it exerts under given conditions when employed 
for traction purposes, will, however, be seen later when dealing with 
the application of motors to traction. 

Energy expended. — The total energy expended in any given 
case of traction, it will be found, can be divided practically at the 
most into three forms of energy. Thus in the example just given — 

Kinetic Energy. — The 169,400 foot-lbs. of energy expended 
during the 10 seconds in giving the car a speed of 15 miles per hour, 
or a speed of 22 feet per second, will be stored up in the car by virtue 
of its motion. This energy is termed the " kinetic energy," or simply 
the energy of motion. This energy, it may be said, will have to be 
either transferred to some other body, or transformed into some other 
form of energy, as will be seen later when dealing with brakes, before 
the car can be brought to rest. The kinetic energy of a moving body 
is generally calculated, not as indicated above, but from the speed and 
weight of the moving body, as will be indicated later. 

Heat Energy. — The 27,500 foot-lbs. of energy expended during 
the 10 seconds in overcoming the various frictional resistances will 
have been transformed chiefly into heat energy, and this energy is 
practically lost as far as recovery and useful purposes are concerned. 

Potential Energy. — The 123,200 foot-lbs. of energy expended 
during the 10 seconds in overcoming gravitational effects, that is, in 
raising the car \}§-, namely, 5|^ feet, will be stored up in the car as 
what is termed so much potential energy, that is, energy which the 
car simply has by virtue of its position, this energy being available 
for use if the car be allowed to descend the 5|- feet either on this or 
some other gradient. 

When a car descends a gradient, this energy, less what is required 
for friction, becomes converted, if not otherwise utilized, into kinetic 
energy, or simply energy of motion, the car, in other words, gaining 
speed. 

Draw-bar Pull. — In cases of traction where the carriages or cars 
are hauled by some external means, such as a steam or electric 



100 ELEMENTS OF ELECTRIC TRACTION 

locomotive, the locomotive is attached to what is termed the draw-bar 
of the carriages, and in consequence the actual pull exerted on the 
carriages by the locomotive is termed the draw-bar pull. This same 
term is also employed where the motors are connected to the 
axles of the car itself, such as in the ordinary electric tramcar, 
although the force or pull is not exerted in the same way. The 
draw-bar pull in these cases refers to the equivalent force or pull 
that the motors exert on the car. This pull is also sometimes termed 
the horizontal effort, or the tractive effort, referring then to the total 
tractive effort exerted on the car, and not simply the tractive effort 
required for friction. Thus, in the example just previously given, the 
motors would have to exert a horizontal effort tending to move the 
car equal to an actual draw-bar pull of 2910 lbs. 

In order to determine the exact relation between the torque as 
exerted by the armature on the armature shaft, and the horizontal 
effort or draw-bar pull as exerted on the car tending to propel it 
forward, it will be necessary first of all to explain the method of 
coupling the motors to the driving axle of the car. 

In order to keep the over-all size of the motors within reasonable 
limits, and suitable for the restricted space in which they have to be 
placed, a higher speed has to be adopted than is suitable for the 
direct connecting of the motors on to the car axles. 

Gearing. — To reduce the speed of the motors to some suitable 
driving speed for the axles, gearing is employed, and the arrangement 
generally adopted in tramway work is as follows : — 

A small toothed wheel or pinion is keyed to the armature shaft, 
and this gears with a spur wheel, as it is termed, which is keyed to 
the same axle as the driving wheels. This arrangement is termed a 
single-reduction gear. 

If the pinion has 14 teeth, and the spur wheel 70, it will be seen 
that the pinion will make five revolutions to the spur wheel's 
one. Such a gear is said to have a ratio of 5 to 1, and the result of 
this gearing will be that the driving wheel will make only I the 
number of revolutions that the armature does in any given time. 
The ratio generally adopted in tramway work varies between 4 and 5 
to 1. 

In Fig. 26 is shown the different speeds and torques that the 
armature and driving axles would have with driving wheels 30 inches 
diameter, and a gear ratio of 5 to 1, when the car to which they are 
attached is travelling at a speed of 10 miles an hour, and a draw-bar 
pull of 800 lbs. is being exerted. 

Now, it must be clearly understood that the introduction of gearing 
in this way does not affect the actual available H.P., with the 
exception that the gearing and additional bearings will introduce a 
little more friction, and a certain amount of power will have to be 



MECHANICS OF TRACTION 



lOI 



spent accordingly in overcoming the additional resistance set up by 
such friction. 

Consequently, if, in measuring the B.H.P. output of the motors, 
the brake be applied to a pulley fixed, not to the armature shaft, but 
on the driving axle, then the B.H.R output with a given current and 
voltage will be found to be a little less, possibly some 5 or 6 per cent.. 



D.B. PULL 
<-600LBS 



10 MILES PER 
HOUR 



^,c,^£VS:Pf/?^^^ 




->THRUST ON RAILS 800LBS 



FiQ. 26. 



than that actually measured on the armature shaft without the 
gearing, under the same conditions of current and voltage, the 
amount less being accounted for as indicated above. 

It should, however, be noted, with the introduction of gearing in 
this way, that while the speed of the driving axle is less than the 
spbed of the armature, the torque exerted on the driving axle will be 
correspondingly greater. The reason for this simply following from 
the principle of work, the greater torque at the lesser speed exerting 
the same power as the lesser torque at the higher speed. 

Thus, with a gear ratio of 5 to 1, while the driving wheels will 
only revolve with J the number of revolutions per minute that 
the armature does, the torque exerted on the driving axle will 
be approximately 5 times that exerted on the armature shaft — 
actually some 5 per cent, or 6 per cent, less than 5 times, owing to 
a torque or twisting effort being required to overcome the resistance 
set up by the extra friction introduced with the gearing. 



102 ELEMENTS OF ELECTRIC TRACTION 

Relation between Torque and Draw-bar Pull. — In tramway 
work there are generally two motors, each being connected to a 
driving axle. In the following explanation, simply one driving axle, 
and the one motor connected with it, will be considered. Now, if 
the torque, say, in Ibs.-feet exerted on the driving axle be divided 
by the radius in feet of the driving wheel, then the total force in 
pounds that one motor exerts at the rim or periphery of the driving 
wheels tending to twist the driving axle round, will be obtained, 
since torque is force multiplied by leverage. 

Thus, if the torque exerted on the one driving axle were 1000 
Ibs.-feet, and the driving wheels 30 inches in diameter, that is, 1^ feet 
radius, the total force exerted by the one motor at the rim of the 

driving wheels will be -^tj— ; that is, 1000 x f , namely, 800 lbs. 

As there are two wheels on each axle, this really means a force of 
400 lbs. at the rim of each. To prevent confusion, however, the 
total force of 800 lbs. will simply be spoken of as though it were 
acting simply on one wheel, this one wheel simply then being 
considered. 

Now, the value of this force of 800 lbs. in this particular example 
is also the value of the force that is at work tending to propel the 
car forward ; in other words, it is the value of the horizontal effort as 
exerted by one motor. 

The reason for this can readily be seen on referring to Fig. 27. 
Assuming the car to be a fixture, and the rails the moving part, it 
will be seen that a force of 800 lbs., acting at the rim of the driving 
wheels in the dii^ection shown, will exert (assuming no slip of wheels) 
an equal and opposite force of 800 lbs., tending to move the rails back 
as shown. Now, the value of the force tending to move the rails 
back is also the value of the force at work tending to move the car 
forward. In other words, with rails fixed and a car free to move, a 
total force of 800 lbs. acting at the periphery of the wheels will 
produce a horizontal effort or draw-bar pull also equal to 800 lbs. 

It will now be seen that with driving wheels 30 inches in diameter, 
the value of the draw-bar pull in pounds (assuming no slip of wheels) 
will always be J that of the number expressing the value of the 
torque in Ibs.-feet exerted on the driving axle. 

Again, with a gear ratio of 5 to 1, and driving wheels 30 inches in 
diameter — since the torque at the driving axle will be practically 
5 times that exerted on the armature shaft — the value of the draw- 
bar pull in pounds will be practically 5 x |, namely, 4 times that of 
the number expressing the value of the torque in Ibs.-feet exerted 
on the armature shaft. For example, see torques exerted as shown 
in Fig. 26. 

Thus there is always a definite connection between the number 



MECHANICS OF TRACTION 



103 



expressing the draw-bar pull, and the number expressing the torque 
exerted, say, on the armature shaft ; the smaller the driving wheels, 
or the greater the gear ratio, the greater will be the draw-bar 
pull for a given torque on the armature shaft, and the greater 
will be the number expressing the ratio between the value of these 
two quantities. 

Consequently, if in any given case the torque be doubled, the 



SOOlbs pulk 




Fig. 27. 



draw-bar pull will also be doubled, or if the torque be made ^ as 
great, the draw-bar pull will also be made ^ as great, and so on. 

As the torque exerted by a motor primarily depends upon the 
strength of current flowing through the armature, and upon the 
strength of field, so also will the draw-bar pull depend primarily 
upon the same two quantities. 

Thus an increased draw-bar pull can only be brought about, either by 
an increase in the value of the current passing through the armature, 
or by an increased field strength, or by an increase in both, and vice 
versa. It should also be added that, as in an ordinary series motor 
the field strength is primarily determined by the armature current, 
an increased draw-bar pull in any given series motor can only be 
brought about by an increase taking place in the current passing 
through the motor, and vice versa. 

With two motors attached to the car, it must be noted that the 



104 ELEMENTS OF ELECTRIC TRACTION 

total draw- bar pull will be twice that due to one motor, assuming, of 
course, that each motor is doing an equal amount of work. 

Adhesive Force. — It will be seen from what has been said 
above, that whatever force there is at work tending to move a car 
forward, there is always at work an equal and opposite thrust on the 
rails, tending to move them back. 

In the example given above, with one motor exerting a draw-bar 
pull of 800 lbs., there would really be, due to this one motor, a force 
of 400 lbs. tending to drive each rail backward, assuming each wheel 
was doing its equal share of work. 

It may be noted here that in horse traction the thrust takes 
place, not on the rails, but on the setts, whereas in electric traction the 
thrust is taken by the rails, hence the wear and tear that takes 
place. 

It has already been seen that were it not for friction between 
the wheels and the rails, the wheels would slip and motion of 
the car would not take place, as no thrust on the rails could be 
obtained. 

The resisting force due to the friction existing between the wheels 
and the rails is termed the adhesive force. The total adhesive force, 
it will now be seen, must be greater than the total tractive effort. 
Thus, if the total adhesive force in the above case were 700 lbs., then 
a total tractive effort of 800 lbs. could not be exerted, the friction 
between the wheels and the rails not being able to sustain a thrust of 
anything greater than 700 lbs., any greater thrust than this causing 
the wheels to slip. The adhesive force existing between the wheels 
and the rails, it is found, depends not only upon the weight upon 
each driving wheel, but largely upon the condition of the surface of 
the rails. If the rails are only slightly wet, for instance, the adhesive 
force is very much reduced, the rails then being in a greasy condition. 
The application of sand in such cases causes the adhesive force to be 
increased. 

In railway work it has been found that the adhesive force varies 
roughly from 400 lbs. per ton weight on driving wheels under average 
conditions to under 200 lbs. per ton under bad conditions. 

Romapac System. — With regard to the wear and tear of tram- 
rails mentioned above, this is proving such a serious item in electric 
tramway practice that a compound tramrail is being put forward by 
the Romapac Tramway Construction Company, Ltd. 

In this system, the bottom portion of the rail consists of a steel 
girder somewhat similar to the bottom portion of the ordinary tram- 
rail, and this, together with the bonding, etc., forms the permanent 
portion of the track, and, when once laid, it is not interfered with. 
On the top of the steel girder, which is suitably shaped, is rolled by 
means of a special and patent machine, the grooved steel head portion 



MECHANICS OF TRACTION 105 

of the rail, after the bottom portion of the track has been laid. Thus 
the rail as a whole consists of two portions. The top portion is 
rolled on so as to grip each side of the steel-girder portion of the 
track, and the grip obtained is of such a character that tests which 
have been made show that a force of some 24 tons is required to slide 
a 1 foot length of the top portion off the bottom portion. The head 
portion, it must also be added, is made to the same specification as the 
standard rails, and is therefore equally hard. When the rails become 
worn, the top portion is stripped off by means of the patent rolling-on 
and cutting-off machine, and the new head portion rolled on as before 
on site. 

The advantages claimed for this system are that, in the renewing 
of the track, only the worn-out portion of the rail has to be renewed. 
A saving of some 50 per cent, in the weight of renewable material, 
and also a saving of some 50 per cent, in the actual cost of renewing 
the track, is in this way claimed. There is also a considerable saving 
in time and labour, and less upset of road and traf&c in the process, 
as only the top setts on each side of the rail have to be taken up when 
the track is being renewed. 

A longer life is also claimed, as the joints of the top portion 
overlap those of the girder portion, and in this way a practically con- 
tinuous track is obtained, with an increased life in consequence. 

Measurement of Draw-bar Pull, etc. — Makers, when plotting 
in the form of curves the results of a complete test of a motor, such 
as is generally made, generally plot, in place of the torque exerted 
say on the driving axle, the equivalent draw-bar pull the motor 
would exert under the same conditions as regards current, etc. Also, 
they generally plot, in place of revolutions per minute say of driving 
axle, the equivalent speed in miles per hour the car would have when 
the driving axles were making this particular number of revolutions. 

As a rule, these tests are made by supplying the motor with a 
constant voltage, generally 500 volts, and noting the speed, also the 
amperes taken by the motor, etc., etc., when various draw-bar pulls 
are being exerted. 

Speed. — If the size of driving wheels and number of revolutions 
they make be known, it is simply a matter of calculation to find the 
speed a car would have if these wheels were attached, and. were 
making this given number of revolutions. 

Thus, if the circumference of the driving wheel in feet be multi- 
plied by the revolutions made in one hour, the number of feet a car 
would travel during the hour at this particular number of revolutions 
will be obtained, and this, divided by 5280,* will give the speed in 
miles per hour. 

From this the following approximate rule is obtained : — 

* 5280 feet = 1760 yards = 1 mile. 



io6 ELEMENTS OF ELECTRIC TRACTION 

Eadius of driving wheel in feet X revs, per min. of driving axle 

14 
= speed in miles per hour 

Draw-bar Pull. — From what has already been said, it will be 
readily seen how the actual draw-bar pull a motor is capable of 
exerting under any given condition of current, etc., can be experi- 
mentally determined from the motor itself. All that need be done 
is to test the motor in a similar way to that indicated in Chapter VI. 
for measuring the B.H.P. ; in fact, this would be done when making 
the complete test for B.H.P., speed, etc., etc., with varying values of 
current as mentioned above. Thus, if the brake be applied to a 
pulley on the driving axle, that is, if the B.H.P. be measured through 
the gear, the draw-bar pull can either be obtained direct from the 
particulars taken during the test, or it may be simply calculated from 
the B.H.P. the motor exerts under any given conditions. 

Thus, if the pulley on the driving axle is the same size as the 
driving wheel, the effective pull in pounds, that is, the difference 
between the pulls exerted on each side of the pulley, will give the 
value of the draw-bar pull in pounds that would be exerted under 
exactly the same conditions as regards current, etc., by this one motor. 

On the other hand, if the B.H.P. simply be known, the draw-bar 
pull exerted under the same conditions (assuming no slip of wheels) 
can readily be calculated thus — 

As— 

Torque in lbs. -feet at driving axle = 



rev. per minute of driving axle 

And as — 

-p. , n . 11 torque in Ibs.-feet exerted at driving axle 

Draw-bar pull m lbs. = — ,. ^ , . . -, — :r--- — ?-t ■ 

^ radms oi driving wheel m leet 

Draw-bar pull in lbs. = 

B.H.P. X 5252 

revs, per min. of driving axle X rad. of driving wheel in feet 

In this way, if B.H.P. exerted at driving axle and revolutions per 
minute and radius of driving wheels be known, then the draw-bar 
pull that will be exerted under these same conditions can be 
calculated. 

Another modification of the above gives the following rule, or 
formula, for connecting total D.B. pull, speed, and total H.P. expended. 

Thus— 

D.B.P. X speed in miles per hour __ tt p 
~375 -M.i. 



MECHANICS OF TRACTION 107 

Example. — Thus, in the detailed example previously given, with a 

draw-bar pull of 2910 lbs., and a speed of 7^ miles per hour, the 

2910 X 15 
H.P. being expended on the car at that instant will be —^w^ o~ 

= 58-2 H.P. 

The H.P. calculated is the B.H.P. that will have to be exerted 
by the motors when this particular draw-bar pull is being exerted at 
this particular speed. 

The H.P. so calculated, it must be noted, is the actual H.P. exerted 
at the particular instant the draw-bar pull and speed have these 
particular values, for just as either pull or speed, or both, might vary 
from instant to instant, so also would the H.P. vary. 

In the above example it means, for instance, that if the pull and 
speed were kept constant for 1 minute, 58*2 x 33,000 foot-lbs. of 
work would be done during that minute. 

The following formulae, which have been deduced on similar lines 
simply from first principles, together with those already explained, 
will be found to be of use in dealing with traction problems : — 

A = amperes passing down the trolley pole. 
V = volts pressure at trolley wire. 
S = speed of car in miles per hour. 
K = radius of driving wheel in feet. 
D = diameter of driving wheel in feet. 
T = total torque in lbs. -feet as exerted by the motors on 
the driving axles. 
D.B.P. = total draw-bar pull in pounds as exerted by the motors. 
N = number of revolutions per minute of driving axle. 
H.P. = horse-power expended in traction. 

a N X E . , CI N X Pt 

S = -^j-, more accurately S =-j^:^^ 



S = 
H.P. = 



T 
D.B.P. = ^ 



N X D , , ^ N X D 

— 2g — , more accurately S = ^^.^^ 

D.B.P. X S 
375 

K 



The following have been worked out on an assumption of a total 
efficiency of 80 per cent. : — 



io8 ELEMENTS OF ELECTRIC TRACTION 

A X V A X V 

T = — ^;^: — X 5-6, more accurately T = — ^ — x 5-63 



T = 



AxVxR ,,^ AxVxE 

rr-~^, , more accurately T = ,^ .^^ 

2*58 -' 2-48S 



D.B.P. = ^ ^r. , more accurately D.B.P. = ^ ,^ 
2-5S -^ 2-48!S 

H.P. = gg^ , more accurately H.P. = ^g^,^ 

Varying Draw-bar Pull. — At the beginning of this chapter it 
was stated that, apart from the force required to overcome frictional 
and gravitational effects, no force was required simply to maintain a 
car at any given speed. This should always be borne in mind in 
dealing with the varying D.B. pull that may be applied to a car. 
Consequently, when the D.B. pull becomes equal to, or just 
balances, the force required to overcome the various frictional 
resisting forces if the car is on the level, or the various frictional 
resisting forces and gravitational effect if the car is mounting a 
gradient, the car will either be at rest, or, if moving, will be travelling 
at some uniform speed. In short, no acceleration or retardation of 
the car will be taking place. 

If the car is in motion, and the D.B. pull exceeds the frictional 
and gravitational forces, then the car will be in a state of acceleration, 
that is, it will be gaining speed. 

To illustrate this, two simple cases will be taken, and the effects 
produced by varying D.B. pull considered — 

1. That of a car running on the level. 

2. That of a car mounting a gradient. 

1. Car running on the Level, Friction neglected. — In order to 
show exactly the effects produced by friction in dealing with the 
motion of a car, an imaginary case will first of all be considered in 
which friction will be assumed not to exist. 

If no friction of any kind whatever existed, the slightest D.B. 
pull would set a car in motion, and would give to the car a small 
but definite acceleration, depending, as already seen, simply upon 
the total weight of car and upon the D.B. pull applied. 

If, now, in such a case, a D.B. pull of 1540 lbs. — see previous 
example — were applied to a 10-ton car starting from rest, the car 
would have given to it, as long as this D.B. pull remained constant, 
an acceleration of IJ miles per hour per second, and at the end of 
10 seconds the car would have attained a speed of 15 miles per 
hour. 

The different effects which would be produced by varying the 



MECHANICS OF TRACTION 109 

D.B. pull at this stage of the car's motion will now be considered. 
To make the case as simple as possible, it will be assumed that the 
changes in the D.B. pull take place not gradually, but instan- 
taneously. 

If now at this stage, that is, after the 10 seconds, the D.B. pull 
were suddenly increased to 3080 lbs., that is, just twice its previous 
value, the acceleration would also be suddenly increased from IJ to 
3 miles per hour per second. 

With a constant D.B. pull of 3080 lbs., the car would gain during 
the next 5 seconds an increase in speed of 3 x 5, namely, 15 miles 
per hour, so that at the end of 15 seconds from the start, the car 
would have attained altogether 15 + 15, namely, a speed of 30 miles 
per hour. 

If at the end of the 10 seconds the D.B. pull had, instead, been 
suddenly decreased to 770 lbs., that is, just half its previous value, 
then with this accelerating force at work the car would still go on 
gaining speed, but only now at the rate of f miles per hour per 
second, and if the D.B. pull of 770 lbs. were kept constant, the 
car during the next 5 seconds would gain an increase in speed of 
f X 5, namely, 3| miles per hour, so that in this case the car would 
have at the end of the 15 seconds, 15 + 3|, namely, a speed of 18| 
miles per hour. 

Thus, while the acceleration in this case will depend with constant 
load simply upon the accelerating force at work, the speed will 
depend not only upon the value of the various accelerating forces, 
but also upon the length of time these various forces have been at 
work. 

If now, on the other hand, at the end of the 10 seconds the motors 
had ceased to exert a D.B. pull, then as the speed at that instant 
was 15 miles per hour, and no force would be at work after that, 
either accelerating or retarding the motion of the car, the car would 
simply go on travelling at the uniform speed of 15 miles per hour, 
and an opposing force of some kind would have to be applied to stop 
the car. 

Car running on the Level, Friction considered. — Taking now 
the actual case, unless a certain D.B. pull be applied, no motion of 
the car will take place owing to friction, and any force that may be 
applied over and above that required for friction will be available 
for accelerating the car. 

Thus, with a tractive resistance of 25 lbs. per ton, to give a 
10 -ton car an acceleration of IJ miles per hour per second, will now 
require a D.B. pull of 250 + 1540, namely, 1790 lbs., a greater 
D.B. pull than in the previous case, owing to frictional resistance. 
Now, as long as this effective force of 1540 lbs., namely, the amount 
over and above that required for friction, is constant, so long also 



no ELEMENTS OF ELECTRIC TRACTION 

will the acceleration be constant, provided, just as before, no increase 
in the total weight takes place, and at the end of 10 seconds the car, 
starting from rest, will have attained with this D.B. pull of 1790 lbs. 
a speed of 15 miles per hour. If now the effective force of 1540 lbs. 
be increased, the acceleration will be increased, and if it be decreased, 
the car will go on gaining speed, but at a correspondingly lesser rate, 
just as in the previous case. 

The acceleration in this case will depend not only upon the D.B. 
pull and total weight of car, but also upon the frictional resistance. 
If at any instant the D.B. pull becomes just equal, that is, just 
balances the frictional resisting forces, the car will continue tra- 
velling at whatever speed it may have at the instant the forces 
become so balanced. Thus, in the above case, if at the end of 
the 10 seconds the D.B. pull is suddenly reduced to 250 lbs., the 
car will continue travelling at the rate of 15 miles per hour, as 
long as the D.B. pull of 250 lbs. total load carried and frictional 
resistances are not varied. It should, however, be noted that any 
increase that may take place in the frictional resistance, such as may 
arise due to increased air resistance, will have the effect of reducing 
the effective force. 

Where high speeds are adopted, as in railway work, an increase of 
friction in this way takes place, and this may reduce the effective 
force until all acceleration ceases. 

If the motors cease to exert a D.B. pull, the frictional resisting 
forces will act as a retarding force, and the car will gradually slow 
down. In this case the kinetic energy of the car is simply trans- 
formed, due to friction, into heat energy, which will be dissipated in 
various ways. The length of time it takes the car to come to rest 
after the D.B. pull is removed will depend upon the frictional 
resistance, and, to shorten this time, other frictional forces in the 
shape of brakes may be introduced. 

2. Car mounting a Gradient. — In this case, before motion can 
take place, not only will a force have to be applied to overcome 
frictional resistance, but, in addition to this, a force will have to be 
applied to balance the particular gravitational pull due to the 
particular gradient the car is on, and any force applied over and 
above this will then be available for accelerating the car. 

Thus, with a tractive resistance of 25 lbs. per ton, as already 
seen, a D.B. pull of 2910 lbs. will be requii'ed to give a 10-ton car 
an acceleration of 1-^ miles per hour per second on a gradient of 2o-> 
a greater D.B. pull than in the previous case, owing to the car being 
now on a gradient. 

If the 250 lbs. required for friction and the 1120 lbs. required 
for balancing the gravitational pull be deducted from the total 
D.B. pull of 2910 lbs., a nett accelerating force, it will be seen, 



MECHANICS OF TRACTION iii 

of 1540 lbs. will be left, which force will give to the car an 
acceleration of 1^ miles per hour per second just as before. 

Now, as long as this effective force of 1540 lbs. is constant, so 
long also will the acceleration be constant, provided no increase in 
the total weight takes place, and at the end of 10 seconds the car, 
starting from rest, will have attained a speed of 15 miles per hour 
on this particular gradient with this particular D.B. pull of 2910 lbs. 
Any increase or decrease in the effective force of 1540 lbs. will bring 
about, just as before, an increase or decrease in the acceleration, and 
as long as this effective force remains constant, so long also will the 
acceleration remain constant, provided no increase in the total weight 
takes place. The acceleration in this case, it will be seen, depends 
not only upon the total D.B. pull, total weight of car, and frictional 
resistance, but also upon the value of the gradient. 

A comparison may now be made between the various D.B. pulls 
required in the three cases; in each case the same acceleration of 
1^ miles per hour per second is given to a 10-ton car — 

On the level, friction neglected . . 1540 lbs. D.B. pull. 
On the level, friction included . . 1790 „ „ 

On a gradient of 20-^ friction included . 2910 „ „ 

If now at any instant the D.B. pull just becomes equal to the 
gravitational pull and the various frictional forces, the car will 
continue moving up the gradient at whatever speed it has at the 
instant the forces became so balanced, and it will neither gain nor 
lose speed as long as the balance exists. If, in the above case, for 
instance, at the end of 10 seconds the D.B. pull is suddenly reduced 
to 250 + 1120, namely, 1370 lbs., the car will go on travelling up 
this particular gradient at the speed of 15 miles per hour as long as 
the D.B. pull of 1370 lbs., total weight of car, gradient, and frictional 
resistance, do not vary. 

If the motors cease to exert a D.B. pull, not only will the 
frictional resistance tend to retard and so stop the car, but the 
force due to gravitation will also be at work, tending to stop 
the car. In this way, the car will come to rest in a shorter time 
on a gradient, depending upon the value of the gradient, than when 
on the level. The gravitational force, it must also be noted, will not 
only assist in retarding the motion of the car, but it will also, if the 
gradient be sufficiently steep, restart the car in motion in the reverse 
or downhill direction. 

In such cases, frictional resistance, in the shape of brakes, will 
have to be applied in order to hold the car on the gradient, and 
so prevent such action. 

In the above example, for instance, a force of 1120 — 250, namely, 



112 ELEMENTS OF ELECTRIC TRACTION 

870 lbs., would be available for accelerating the car in a downhill 
direction. 

In stopping a car in this way on an incline, the kinetic energy 
of the car is partly transformed into heat energy, due to frictional 
resistance, and part is transformed into potential energy, the car's 
own motion carrying it forward up the incline, and so raising the 
car some definite number of feet. 



Examples 

(1) A car travels 100 yards in 15 seconds. 
What is the speed of the car, expressed — 
(a) In miles per hour ? 

(h) In feet per minute ? 

(a) A rate of 100 yards per 15 seconds is equivalent to a rate of 

400 yards per 60 seconds, also to a rate of 24,000 yards per 
hour ; 
.*. equivalent rate = -^f^(y =13*6 miles per hour 

Therefore the car is travelling at the rate of 13*6 miles per hour. 

As a rough rule, divide twice the number of yards by the number 
of seconds, and the result will give the approximate speed in miles 
per hour ; thus — 

— q-^ — = 13*3 miles per hour 
15 

(b) A rate of 100 yards per 15 seconds is equivalent to a rate of 

400 yards per minute, also to a rate of 1200 feet per minute. 

Therefore the car, when travelling at a speed of 13*6 miles per 
hour, is travelling also at the rate of 1200 feet per minute. 

(2) A car is given a uniform acceleration of 2 miles per hour per 
second. 

(a) What speed will the car attain, starting from rest, in 6 seconds ? 

(b) What number of yards will the car travel during the 6 seconds ? 

(a) As increase of speed is 2 miles per hour every second, there- 
fore in 6 seconds the car will have increased its speed 6x2, 
namely, 12 miles per hour 

Therefore, starting from rest, the car in 6 seconds will attain a 
speed of 12 miles per hour. 



MECHANICS OF TRACTION 113 

(b) As at the end of 6 seconds the speed is 12 miles per hour, 
the average speed has been ^-, namely, 6 miles per hour. 

.*. in 6 seconds the car will travel ^ ^ = yj^ part of a mile 

As yjfj mile = 17*6 yards, the car therefore travels 17*6 yards 

Therefore the car with the above acceleration will travel in the 
6 seconds a distance of 17*6 yards. 

This could have been calculated much more easily from the 
approximate formula given in Chapter X. ; thus — 

AT^ 

If acceleration and time were simply known, then, as Y = —-p 

(see page 175) — 

Y = J =18 yards approximately 

or, if speed at end of 6 seconds and acceleration were known, as — 

S2 = 4AY /. 12 X 12 = 4 X 2 X Y 
.*. 8Y = 144 .-. Y = 18 yards, as before 

(3) A car is given an acceleration of 4 feet per second per second. 
"What is the value of the acceleration expressed in miles per hour 

per second ? 

An increase of 4 feet per second every second is equivalent to 
an increase of 4 x 3600, namely, 14,400 feet per hour per 
second. 

As 14,400 feet = -L4^%Q miles, namely 27 miles 
.*. 14,400 feet per hour per second = 2*7 miles per hour every second 

Therefore an acceleration of 4 feet per second per second is 
equivalent to an acceleration of 27 miles per hour per second. 

(4) A car travelling at 20 miles an hour is pulled up in 40 feet. 
What is the value of the retardation in miles per hour per 

second, assuming it to have been uniform ? 

Average speed in slowing down = -2^, namely, 10 miles per hour 
A speed of 10 miles per hour is equivalent to a speed of — 
10 X 5280 , ^._„ ^ 

60 y 60 ' ^^^^^y> 14^ i6^t per second 

40 
/. time taken to travel the 40 feet = yj;^ = 274 seconds approx. 

20 
.*. retardation = T^^ffi "^ ^'^ miles per hour per second approx. 

Therefore the retardation in the above case will be 7-3 miles per 
hour per second. 

I 



114 ELEMENTS OF ELECTRIC TRACTION 

By means of the approximate formula given in Chapter X., this 
could be calculated much more easily thus — 

As 40 feet = 13-3 yards 

and as A = -r^ 
4Y 

, , ^. 20 X 20 400 

retardation = . ■ ■■ ..o o = ftttt 

4 X 13-3 53*2 

= approximately 7" 5 miles per hour per 
second 

(5) It is required to give an acceleration of 2 miles per hour per 
second to a 6-ton car mounting a gradient of 1 in 14. 

What draw-bar pull would be required, assuming a tractive 
resistance of 25 lbs. per ton ? 

As 102*6 lbs. per ton are required to give an acceleration of 

1 mile per hour per second, 
.*. 205*2 lbs. per ton will be required to give an acceleration 
of 2 miles per hour per second. 

.-. force required for accelerating l ^ ^ 
purposes J 

force required to balance! ._ 6 x 2240 _ ^^^ 

gravitational effects J 14 ~" " 

force required to overcome \ _ c^f- n _i-n 
tractive resistance | - ^5 X b _ iDU „ 



.*. total draw-bar pull = 2341-2 



Therefore the draw-bar pull required under above conditions 
= 2341 lbs. approximately. 

(6) Each of the two series motors on a car under certain 
conditions exerts 25 B.H.P. at the armature shaft when the armature 
is making 555 revolutions per minute ; the gear ratio is 4*78 to 1, and 
the driving wheels are 33 inches diameter. 

(a) What torque in Ibs.-feet does each motor exert on the 
armature shaft ? 

(b) What torque in Ibs.-feet does each motor exert on the driving 
axle (neglecting friction of gear) ? 

(c) What will be the D.B. pull in pounds due to each motor ? 
{d) What speed in miles per hour will the car have under the 

above conditions ? 



MECHANICS OF TRACTION 115 

(a) . . As torque m Ibs.-ieet = -. 

^ ^ rev. per minute 

25 X 5252 

/. the torque exerted by one motor = =W^-^ = 236"57 lbs. -feet 

000 

Therefore the torque exerted by one motor under above conditions 
on the armature shaft = 236*57 lbs. -feet. 

(b) With a gear ratio of 478 to 1— 

The torque exerted on the driving axle (neglecting friction of 
gear) = 236-57 X 4-78 = 1130-8 Ibs.-feet. 

Therefore the torque exerted by each motor on the driving axle 
under above conditions = 11 30*8 Ibs.-feet. 

(c) With driving wheels 33 inches diameter or 16 J inches radius, 

that is, 1*375 feet radius — 



The total force exerted at the rim of) 1130-8 
the two driving wheels ) 1'375 



•^o 



= 822-4 lbs. 



Therefore the D.B. pull exerted by each motor under above 
conditions = 822*4 ^bs. 

This could also be worked out from the formula — 

D.B.P. in lbs. = ?i^^^^*^^^ (See page 106.) 

555 
As N =-7yjn, namely, 116 revolutions per minute approx., 

D.B.P. in lbs. = -r^-^— — TTon^ = 823 lbs. approximately as before 

(d) As 33 inches diameter = 33 x 3-14, namely, 103-62 inches 

circumference or 8*63 feet circumference, 

The car will travel 8-63 feet for every revolution of the driving 

axles (assuming no slip). 

As the armature makes 555 revolutions and the gear ratio is 

4-78 to 1, 

555 
The driving axles under these conditions will make 77=^, namely, 

116 revolutions per minute approximately. 
.*. in 1 minute the car will travel a distance of 8-63 x 116, 
namely, 1002 feet approximately. 

1002 feet per minute = rc^nr^ — miles per hour 

= 11-4 miles per hour approximately 



ii6 ELEMENTS OF ELECTRIC TRACTION 

Therefore under above conditions the car will travel at a speed of 
approximately 11*4 miles per hour. 

This could also be worked out more easily by the approximate 
formula — 

S='^^ (See page 107.) 
.*. S = .. ■ = 11-4 miles per hour approximately as before 

(7) A car is supplied with 50 amps, at a pressure of 500 volts, 
assuming an efiQciency of 80 per cent, for the motors and gearing. 

What D.B. pull under these circumstances will the motors exert 
when the car is travelling at 10 miles per hour ? 

As D.B. pull in pounds with an efficiency of 80 per cent. 

Ax V . - 

^ 2-5 X s ^pp^o^'^i^^^t^iy 

/. D.B. pull = ^^^^-^- = m- = 1000 lbs. 
^ 25 X 10 ^^ 

Therefore with an efficiency of 80 per cent., the motors under 
the above circumstances will exert a D.B. pull of 1000 lbs. 
approximately. 

(8) A 10-ton car is mounting a gradient of 1 in 12 at a speed 
of 8 miles per hour, and the resistance to traction under these 
circumstances is 30 lbs. per ton. 

(a) What D.B. pull will be required simply to maintain the car 
at the uniform speed of 8 miles per hour ? 

(h) What H.P. would the motors be exerting under these circum- 
stances ? 

(c) What amperes would the car be taking, assuming an efficiency 
of 80 per cent, and that the trolley pressure is 500 volts ? 

(a) D.B. pull required to overcome resistance to traction 

= 10 X 30 = 300 lbs. 

D.B. pull required to balance gravitational pull 

= = 2a^oo _. iSQQ it>s. approximately 

.-. total D.B. pull = 2166 lbs. 

Therefore D.B. pull required simply to maintain the car at the 
uniform speed of 8 miles per hour = 2166 lbs. 



MECHANICS OF TRACTION 117 

(b) . . As H.P. =^:5iZ^lfiP2id 

• HP— ^ — 1TL3 2 8 _ Aa-0 

, . n.r. _ ^f^ _ -^75- -- ^t> z 

Therefore the H.P. exerted by the motor under the above con- 
ditions would be 46 -2 H.P. 

A X V 

(c) As D.B. pull with an efficiency of 80 per cent. = -^7= — ^ 

D.B.P. X 2-5 X S 

Amperes = ^ — 

2166 X 2-5 X 8 2166 x 20 ^^ ^ 
:. amperes = ^^ = ^^ — = 86'6 amps. 

Therefore the amperes taken by the car under the above conditions 
would be 86*6 amps. 

(9) A 10-ton car with wheels 30 inches diameter is descending 
a gradient of 1 in 10. Assuming a tractive resistance of 24 lbs. 
per ton — 

(a) What retarding draw-bar pull would the motors acting as 
dynamos have to exert to prevent the car being accelerated ? 

(h) What is the total retarding torque they would have to 
exert on the driving axles ? 

(c) What acceleration would be given to the car if the motors 
exerted no retarding force ? 

(d) What speed would the car attain with the motors exerting no 
retarding force in travelling 50 yards ? 

Answer — 

(a) 2000 lbs. 
(h) 2500 Ibs.-feet. 

(c) 1*94: miles per hour per second. 

(d) 19 '9 miles per hour. 

(10) A 10-ton car in descending a gradient of 1 in 10 is main- 
tained by means of the motors (acting as dynamos) at a speed of 
4 miles per hour. Assuming an efficiency of 70 per cent., what 
horse-power would be available for being regenerated or sent back to 
the line if the motors are employed as dynamos for that purpose, 
assuming a tractive resistance of 24 lbs. per ton ? 

Ansiuer — 

149 E.H.P., or its equivalent, 11*1 kilowatts. 



CHAPTER VIII 

CHARACTERISTIC PROPERTIES OF CON- 
TINUOUS-CURRENT MOTORS 

Classification of Motors. — Motors are classified and described by 
the method adopted of exciting the field exactly in the same way as 
for dynamos ; thus there are series, shunt (including those motors 
in which the shunt field is excited separately), and compound motors. 
These different types of motors have their own characteristic properties, 
depending on the method of exciting the field, as will now be seen. 

Shunt Motor. — A shunt motor is, roughly speaking, a constant- 
sp-eed motor, its speed in this way being independent of the load. 
Strictly speaking, however, the speed of a shunt motor drops slightly 
as the load is increased, and of course increases slightly as the load 
is decreased. The variation in speed, however, with a well-designed 
shunt motor is only very small, possibly at the most 5 per cent, or 
so, the variation depending upon the design and size of motor. 

A shunt motor can be run light, that is, without load, and it will 
then have its normal and also its maximum speed. 

If the field terminals of a shunt motor be detached from the 
armature or main terminals of the motor, and the shunt field winding 
be connected to some source of supply quite separately, that is, as a 
circuit distinct in itself, apart from the armature circuit, such a motor 
is sometimes said to be separately excited. The behaviour of such a 
motor is practically identical with that of a shunt motor, the speed 
being practically constant. 

Series Motor. — A series motor is a variahle-sipeed motor, its 
speed varying with, and in this way depending on, the load, running 
more slowly on heavy loads than on light ones. 

On a very light load it will run at an excessive speed, so much 
so that it would be dangerous to run a series motor of any appreci- 
able size without load, the danger being that with the excessive 
speed the centrifugal force would be so great as to possibly " burst " 
the machine. This excessive speed is due to the very weak field 
that exists, and which is the outcome of the light load. 

This danger, it may be said, also exists with any type of motor 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 119 

on light load should the field be weakened in some accidental 
manner, as the breaking of the shunt circuit in a shunt motor. 

On account of the above, it is not advisable to transmit power 
from a series motor by means of a belt, as, in the case of the belt 
coming off or breaking, the machine is left without load ; with chain 
or gear driving the above danger is reduced. 

A series motor is very suitable for starting under heavy loads, 
and is consequently used in crane and traction work. 

Compound Motor. — A compound motor has a combination of 
series and shunt field windings. 

In dynamo construction the object of compounding, as already 
seen, is to obtain either a constant voltage, or a voltage which 
increases with increasing load ; consequently, the series winding is 
arranged to assist the shunt. 

In compounding a motor, the series winding may be arranged 
either to strengthen the main shunt field somewhat — a greater 
strengthening action taking place the greater the current — in which 
case the field is called a cumulative winding, the magnetizing effects 
being added ; or it may be arranged to weaken the main shunt field 
somewhat — a greater weakening action taking place the greater the 
main current — in this case it is called a " differential winding," the 
strength of field being due to the difference of the two magnetizing 
effects. 

Cumulative Compound Motor. — This type of motor is de- 
signed for the purpose of giving to a shunt motor some of the 
characteristics of the series motor, namely, to increase its torque at 
starting, or under- heavy loads, and so enabling it to cope with 
heavy overloads without the danger of being pulled up. The speed 
variation in this type is greater than in a shunt motor, resembling 
more the series. 

Differential Compound Motor. — This type of motor is de- 
signed for running at constant speed. Heavy overloads, however, 
with this type of motor should be avoided, the motor being liable to 
stop when so overloaded, owing to the serious weakening of the main 
field and the consequent reduction of the torque. 

Self-regulating Properties. — An electric motor, in certain re- 
spects, is self-regulating, and before dealing in detail with the various 
characteristic properties of the types used in traction work, the 
general way in which all continuous-current motors regulate them- 
selves will first of all be considered. 

If a series of experiments be made with any of the above types of 
electric motors, fitted, say, with a friction brake similar to that 
already described, so that the load upon the motor can be varied — 
increase of load being brought about by increase of friction; this 
being again brought about by adding additional weights to the 



120 ELEMENTS OF ELECTRIC TRACTION 

belt on the opposite side to the spring balance, so that the greater 
the load the greater the pull the motor has to exert on the belt — 
two main facts will be noticed on running the motors under various 
loads — 

1. Concerning the speed. 

2. Concerning the electrical input. 

1. Speed. — It will be found that an electric motor, if supplied 
with a suitable and constant voltage, will run and continue to run, 
when once it has been started, at some uniform speed as long as the 
load remains constant. 

Variations of load will bring about variations of speed in all the 
above types of motors to a greater or less extent, except those 
specially designed for running at a constant speed ; and where varia- 
tions of speed do take place it will be found that with each load 
the motor will run at some definite and uniform speed, whatever that 
speed may be, as long as that particular load remains constant. 
Consequently, in all these cases variation of speed will only be 
brought about under above conditions by variations in load, the 
motor always having a definite and uniform speed for each definite 
load. 

The load upon the motor in all these cases is assumed to be, of 
course, a suitable one ; that is, within the range and power of the 
motor. 

2. Electrical Input. — It will also be found that the amperes 
passing through the motor under test are constant as long as the 
load is constant, and that the amperes increase and decrease — not 
necessarily in strict proportion — with increase and decrease of load. 
In short, a series of experiments will show that an electric motor is 
self-governing ; that is, the motor itself automatically regulates the 
electrical power put in, so as to correspond with the work done or 
power given out. Thus, it must be very clearly borne in mind that 
while a motor may not be as efficient at light loads as on heavier 
ones, it takes less electrical power, that is, less watts on light loads 
than on heavy ones, no external regulator as far as power is con- 
cerned being required. The consumption of energy always corre- 
sponds with the work done or energy given out by the motor. 
Thus, if the load on a motor is reduced, so also automatically is the 
power reduced, no waste of energy in this way taking place. 

The above experiments thus show that with variable-speed motors 
(whatever be the amount of variation), if the supply voltage be 
constant, a motor will have for every given load a corresponding 
speed and current. 

When a motor is designed for constant speed, it will have for 
every given load a corresponding current, the speed, of course, being 
practically the same for all loads. 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 121 



The reasons for the above self-regulation will now be given, and 
to make the following explanation as simple as possible, those motors 
which vary their speed with variation of load will simply be con- 
sidered. These types, it might also be added, are the ones chiefly in 
use. In traction work the series motor is chiefly employed, although 
at the present time the shunt type is also being advocated. 

Speed and Power Regulation. — In Fig. 28 a simple case of a 
motor under load is shown, the motor being represented as hoisting 
a weight of 200 lbs. by means of a pulley 
fixed to the armature shaft. To merely hoist 
the weight, the motor would have to exert a 
force equivalent to a weight of 200 lbs. at 
the rim of the pulley, or, better still, if the 
pulley were 3 feet diameter, the motor would 
have to exert a torque or twisting effort of 
200 X li, namely, 300 Ibs.-feet. 

In addition, however, to this, the motor 
would have to exert a force to overcome 
friction and various other resisting forces 
which are set up when an electric motor is 
in motion, and which will be dealt with later. 

To take figures which would be something 
like proportionate to the force under con- 
sideration, a force of 5 lbs., for instance, 
might have to be applied at the rim of the 
pulley to overcome friction, and a further 
force also of 5 lbs. might also be required to 
overcome the other resisting forces men- 
tioned. 

In all, then, the motor would have to exert — 
A torque of 200 lbs. x 1^ feet, namely 300 Ibs.-feet, to 

balance the load ; 
A torque of 5 lbs. x 1| feet, namely 7^ Ibs.-feet, to over- 
come the friction ; 
A torque of 5 lbs. X 1^ feet, namely 7^ Ibs.-feet, to over- 
come the various other resisting forces. 

Thus the motor would have to exert a total torque of 315 Ibs.- 
feet, or, if the reader prefers to deal in forces, a force equivalent to 
210 lbs. — applied, it must be noted, at the rim of the 3-feet-diameter 
pulley. 

Now, the following principle, in dealing with the load and speed 
of a motor, must always be clearly borne in mind, just as in dealing 
with the motion of a car : — 

When the torque exerted by a motor just balances that due to load, 
friction, and the other resisting forces mentioned, set up in and due 




Fig. 28. 



122 ELEMENTS OF ELECTRIC TRACTION 

to the motion of the motor, the motor will run at some uniform 
speed as long as the load, friction, etc., and torque exerted by the 
motor so balance one another, just as a car will continue to run on 
the level at a uniform speed when the draw-bar pull just balances the 
tractive resistance. 

Thus, in the above example, when the motor is running at some 
uniform speed under the above load it will just be exerting a torque 
of 315 Ibs.-feet. 

If, now, half the load were "thrown off" — the motor now only 
having a weight of 100 lbs. to hoist — the torque, exerted by the 
motor, would, at this particular instant, before any re-adjustment of 
current took place, exceed that due to the decreased load, etc. 

The balance of torques would in this way be upset, and, roughly 
speaking, a little less than half the torque the motor was exerting 
at the particular instant the load was thrown off, would be available 
for acceleration. 

The motor would consequently speed up, and in speeding up 
would gradually generate a greater back E.M.F., thus reducing the 
current passing through the motor, and so gradually reducing the 
torque until a balance was reached, namely, when the torque due to 
load, and that required for friction, etc., was just balanced by the 
now reduced torque exerted by the motor. 

The motor would then continue to run at whatever speed it had 
at the instant the torques became so balanced ; that is, in the above 
case, at some higher but uniform and definite speed, corresponding 
with the reduced load. The reduction of current would in this way 
bring about a reduction in the electrical power supplied, thus corre- 
sponding with the reduced load. 

If, on the other hand, the load were increased, yet still within 
the range of the motor, the torque due to the load, etc., would, for 
the time being, be greater than the torque exerted by the motor. 
The motor in consequence would slow down to a greater or less 
extent, depending upon the type of motor. 

In this way the back E.M.F. would be gradually reduced, 
current and torque would in consequence be gradually increased, until, 
as before, the torque due to the increased load, etc., was just 
balanced by the increased torque now exerted by the motor, the 
motor then continuing to run at some slower but uniform and 
definite speed, corresponding with the increased load. 

The increase of current would bring about an increase in the 
electrical power supplied, thus corresponding with the increased load. 

If a considerable overload were put on the motor, there would 
be a corresponding reduction of speed — the actual reduction 
depending upon the value of the load, and upon the type of motor 
employed — and a corresponding considerable increase in the current 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 123 

and the consequent torque, due to the decreased back E.M.F. In 
this way the motor always endeavours to increase its torque to suit 
that of the load. If the load were increased to such an extent as to 
be finally beyond the effort of the motor, the motor in such a case, 
not being able to exert a torque equal to that due to the load, etc., 
would slow down and finally stop revolving. 

The excessive current that would flow under the above circum- 
stances would, of course, ia practice never be allowed, as the 
excessive generation of heat, and consequent excessive rise in tem- 
perature of the windings, if such current were allowed to flow for 
any length of time, would be sufficient to burn the motor out. To 
protect the motor from such excessive overload of current, fuses and 
circuit breakers are generally inserted, as already mentioned. 

Load. — In varying the load in the above experiments, it will be 
seen that the torque or twisting effort exerted by the motor had to 
increase in a corresponding manner with increase of load, the 
greater the pull the motor exerted, the greater being the torque 
exerted. 

Thus, in the sense the term " load " is here used, the torque will 
always be a measure of the load ; that is, a motor exerting a constant 
twisting effort or torque will be said to have a constant load, and 
consequently a varying load will mean a varying torque, the torque 
simply increasing and decreasing with increase and decrease of 
load. 

As applied to traction work, this will mean, in a similar way, 
that a motor fitted to a car with a given ratio of gear wheels, and a 
given size of driving wheels, will be said to have a constant load as 
long as it exerts a constant draw-bar pull ; constant load in this case 
meaning not only constant torque, but also constant draw-bar pull. 

As the horse-power developed by a motor depends not only on 
the torque, but also upon the speed, so it also depends, in like 
manner, not only on the load put on a motor, but also upon the 
speed of the motor. 

Thus distinction must be made between load and power, as, for 
example, the load — in the sense that it is used here — may be so 
great as to prevent the motor working, or, in other words, developing 
any power. 

If the load is so excessive that the motor fails to revolve, then all 
the electrical energy supplied will simply be transformed into heat, 
electrical energy only being transformed into mechanical energy 
when motion takes place, that is, when a back E.M.F. is being 
generated. 

The following analysis will now enable the characteristic 
properties of motors to be dealt with a little more in detail. To 
simplify matters as much as possible, it will be assumed that the 



124 ELEMENTS OF ELECTRIC TRACTION 

torque the motor exerts is simply that required for the actual load 
put on the motor. The motor, of course, really has to exert a greater 
torque than this, in order to overcome friction and the various other 
resisting forces set up. As the resisting forces due to friction, etc., 
only form, however, a small portion of the total load — except when 
a motor is on light load, when they form the sole load — they will, in 
order to simplify matters, be ignored for the present. 

Motor Analysis. — A varying load, as already seen, means that 
a varying torque has to be exerted by the motor. 

Now, the torque exerted by any given motor, that is, a motor 
already constructed, depends simply upon the strength of armature 
current and strength of field. 

The torque, therefore, of a motor can be varied by the varying of 
either — 

(1) Strength of field ; 

(2) Armature current ; or a suitable variation of both. 

(1) Strength of field variation can be brought about by a variation 
in the value of the current passing through the field coils, this being 
again brought about by a variation of either — 

{a) The resistance in the field circuit, 

(6) The volts across the terminals of the field — in a shunt motor 
this will be the supply volts — or a suitable variation of both. 

(2) Armature current variation can be brought about by a 
variation of either — 

(a) The supply volts. 

(fS) The back E.M.F. ; this, with a given motor, depending simply 
upon strength of field and speed. 

(c) The resistance in the armature circuit ; or by a suitable 
variation of any two or all three. 

It should be noted that the torque exerted by a motor depends 
not only upon the strength of field, or, more definitely, upon the 
intensity of the field, that is, upon the number of lines say per 
square inch passing out of the magnets, and upon the armature 
current, but also upon the number and length of the armature 
conductors, and also upon the distance of the conductors from the 
centre of the shaft. 

As the number and length of the conductors and their distance 
from the centre of the shaft cannot be altered when once the armature 
has been constructed, the only way the torque can be altered, as far as 
the armature is concerned, is by a variation in the current flowing 
through the conductors taking place. Again, the intensity of the 
field strength will depend not only upon the magnetizing force at 
work, but also upon any demagnetizing force there may also be at 
work. 

Now, owing to current circulating round the armature core, 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 125 

certain demagnetizing actions are set up which tend to demagnetize 
and so weaken the main field. 

The intensity of the field strength, apart from the above 
demagnetizing force, depends not only upon the current passing 
through the field coils, that is, upon the excitation current, but also 
upon the number of turns of wire in the field coils, and upon the 
length and permeability of the materials forming the magnetic path. 

Here, again, when once a motor has been constructed, the only 
way the torque can be altered, as far as the intensity of the field 
strength is concerned, that is, apart from the demagnetizing force at 
work, is by a variation in the value of the current passing through 
the field coils taking place. 

Variation in the value of the current passing through the field 
coils, and hence variation of field, is brought about, as shown in the 
above analysis, by a variation of either the resistance in the field 
circuit, or the pressure of supply across the field terminals, or by a 
suitable variation of both. In this way, the field strength in any 
given motor will depend, not only upon the pressure of supply across 
the field terminals, and upon the resistance of the field winding, but 
also upon the amount of demagnetizing action taking place. 

To simplify matters, however, consideration of the demagnetizing 
effects will be left until later. 

Shunt Motor. — To apply this analysis to a shunt motor, let it 
be assumed that the motor is supplied with constant pressure, and 
that the resistance in circuit is constant, as would be the case under 
most working conditions, that is, when all starting resistance has 
been cut out. 

If load be varied, a variation in the torque will be brought about 
by a variation in either — 

(1) Strength of field ; 

(2) Armature current ; or a suitable variation of both. 
Strength of Field. — As the supply volts are constant, and also 

as the resistance of the field winding will be practically constant, 
the field strength will be constant. Therefore, in this case, varying 
load will simply mean a variation in the armature current. 

Armature Current. — As the supply volts and the resistance in 
the armature are both constant, it will be seen that the back E.M.F. 
will have to vary in order for there to be any variation in the 
armature current. 

Again, as the field is constant, the speed will have to vary in 
order for there to be any variation in the back E.M.F. 

Consequently, with a shunt motor, under ordinary working 
conditions, variation of load means variation of speed. 

Extent of Variation of Speed. — It only remains now to be 
seen to what extent the speed must vary under the above conditions 



126 ELEMENTS OF ELECTRIC TRACTION 

to bring about the requisite change in the value of the current. This 
speed variation will be found to be very small. 

It must always be remembered in dealing with the current 
passing through a motor, that it is the effective E.M.F. in the motor 
circuit which determines the value of the current. 

As the resistance in the armature circuit after all starting 
resistance is cut out is small, being in shunt motors only the 
resistance of the armature, and in series motors the resistance of 
armature and field — this in machines of any appreciable size will 
only be the fractional part of an ohm — the effective E.M.F. need 
only be, comparatively speaking, small, in order to send a large 
current through the circuit. 

As the effective E.M.F. is the difference between the applied and 
the back E.M.F., a slight decrease in the value of the back E.M.F. 
will bring about a much greater increase in the effective E.M.F. 
Thus, let the line AB (see Fig. 29) represent say the 100 volts of 
supply to a motor, and let the length BC represent the back E.M.F., 
then AC, the difference, will represent the effective volts. Now, to 
double the effective E.M.F. so as to double the current does not 



ACD 



Fig. 29. 

mean reducing the back E.M.F. represented by BC to half its value, 
but only to a value represented by BD, the length AD being equal 
to twice the length AC. The effective E.M.F. is now represented 
by AD. As the speed (the field being constant) is proportional 
to the back E.M.F., it will be seen that a small drop in speed 
corresponding to the slight drop in the back E.M.F. will be sufficient 
to increase the current to twice its original value. Thus a small 
drop in speed in a shunt motor brings about a much greater difference 
in the effective E.M.F., and so a much greater difference in the value 
of the current. Thus a small variation in speed with a large varia- 
tion of load. 

Example. — To take an actual case, the armature resistance of a 
small 100-volt shunt motor is 0'2 of an ohm, its full-load current 
being 10 amps. When running at quarter-full load, namely, when 
2^ amps, are passing through the armature, an effective pressure of 
half a volt is required. The back E.M.F. is therefore in this case 
99^ volts, and the speed, treating the field as constant, proportional 
to 99^. To increase the current to four times its value, that is, to 
10 amps, (the full load), four times the effective pressure is required, 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 127 

namely, 2 volts, the back E.M.F. now being 98 volts, and the speed 
in this case proportional to 98. Thus, as the load is increased from 
quarter-full load to full load, the speed drops proportionately from 
99 J to 98, about IJ per cent. Thus the shunt motor, while it has, 
strictly speaking, a definite and different speed for each different 
load, has a speed variation so small that for many practical purposes 
it can be said to be a constant-speed motor, and that the speed is 
thus independent of the load. 

Variation of Torque with Current. — It has already been 
shown that the torque depends upon strength of field, and strength 
of armature current ; the stronger these are, the greater the torque. 
In a shunt motor, as the field is practically constant, the torque will 
simply vary, with the armature current increasing and decreasing 
practically at the same rate. 

It will be found that if the matter be now looked at from a 
power point of view — the input and output of the motor being 
considered quite separately — the results concerning variation of 
torque and speed with variation of current are in entire agreement. 

Input. — If the current in any given case be doubled, the voltage 
being constant, the electrical power put in will be doubled, and 
therefore the H.P. output should also be approximately doubled. 

Output. — The output of a motor, as already seen, depends upon 
load and speed. 

If with double the current double the torque is obtained, then 
under these circumstances it means that the load has been doubled. 

With double the load, and speed remaining practically constant, 
double the output will be also approximately obtained, the output 
thus corresponding with the input. 

Thus, roughly, in a shunt motor, if in any given case — 

The load is made ..... twice as great. 

In order to obtain — 

A torque ....... twice as great, 

The current will become .... twice as great ; 

The H.P. output will be . . . . twice as great. 

The speed being practically . . . constant. 

Series Motor. — To apply the analysis now to a series motor, 
let it be assumed that the motor is supplied with constant pressure, 
and that the resistance in the armature circuit is constant, as will be 
the case when all starting resistance has been cut out just as before. 
If load be varied, a variation in the torque will be brought about by 
a variation in either (1) strength of field ; (2) armature current ; or a 
suitable variation of both. 

Strength of Field. — As the field winding is in series with the 
armature, whatever current passes through the one will pass through 



128 ELEMENTS OF ELECTRIC TRACTION 

the other, unless some device be adopted of shunting a portion of 
the main armature current through some other path than that of the 
field. It will be assumed, however, that no such device is adopted, 
and that an ordinary series motor such as is used in the ordinary 
series parallel system for traction work is being considered. 

Varying torque, therefore, in this case can only be brought about 
by a variation taking place both in the field strength and in the 
armature current, as the one cannot be varied without the other, 
seeing, for instance, that increased armature current means also an 
increased field strength, and vice versa. Consequently, it must be 
borne in mind that an increase of load will bring about an increase 
in the field strength, and a decrease in load a decrease in field 
strength. 

The value of the current in the series winding, and the consequent 
field strength, will in this case not be determined by considering the 
volts across the terminals of the series winding, or its resistance, but 
by considering simply the armature current. 

Armature Current. — As the supply volts and the resistance in 
the armature circuit are both constant, it will be seen that the back 
E.M.F. will have to vary in order for there to be any variation in the 
armature current. 

Variation in the back E.M.F. may be brought about by a variation 
in the speed, or the field strength, or a suitable variation of both. 

Now, as increase of field strength takes place with increase of 
load, it will readily be seen that a decrease must take place in the 
speed if an increased current is to be obtained, and that especially so 
with an increased field strength. 

The decrease in speed would be very small, just as in the case of 
a shunt motor were the field constant, but with an increased field 
strength a greater reduction in speed must take place, even if the 
same back E.M.F. is to be generated, and the same current to flow 
as originally, therefore to obtain a still greater current a still further 
slight reduction of speed will be required. Thus, the chief cause of 
the great reduction in speed in a series motor with increase of load 
is not so much the increased current required, but is chiefly due to 
the increase in field strength which is the outcome of the increased 
load. 

In a similar way, to decrease the current the back E.M.F. must 
be increased, and this with a weakened field means a considerable 
increase in speed. 

To sum up, with a series motor under ordinary working conditions 
an increase of load will bring about a considerable decrease in speed, 
and a decrease in load a considerable increase in speed. 

It remains now to be seen to what extent the torque, speed, and 
current vary with varying load. 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 129 

Variation of Torque, Speed, and Current with Varying 
Load — At the outset a difficulty arises, owing to the fact that 
doubling the current may or may not mean doubling the strength 
of the magnetic field, and so on, all depending upon the degree of 
magnetization of the field magnets, this again depending upon the 
particular design. 

To form a rough initial idea, however, it will be assumed that 
doubling the current does double the strength of the magnetic 
field.. 

Assume, then, that a given series motor be supplied with some 
constant voltage, and that a given load be applied. It will take a 
given number of amperes, run at some definite speed, and in so doing 
will exert a certain definite torque. If now the load be made four 
times as great, four times the torque will at the least be required. 
If the current be doubled, and the field in consequence be doubled 
in strength by so doing, then the torque will be increased to four 
times its value, which is the value required. Thus, on the above 
assumption, doubling the current has increased the torque to four 
times its value. In a similar way, with half the current only, one 
quarter the torque will be exerted. This rapid increase or decrease 
in torque value, with an increase or decrease in current value, is one 
of the characteristic properties of the series motor. 

Now, before the load was increased, the motor was developing a 
certain back E.M.F., and had the field with increase of load remained 
constant, a very little variation in the speed, as already explained, 
would have been required in order to obtain double the current. 
Owing now to the field being doubled in strength, the speed will 
have to be half its original value, in order to obtain the same back 
E.M.F. and the same current as originally, and consequently a little 
less than half to obtain double the current. 

Thus, on the above rough assumption concerning strength of 
field, if in a series motor in any given case — 

The load is made . . . four times as great, 

In order to obtain — 

A torqiic, . . . . . .four times as great, 

The currc7it need only be . . . twice as great ; 

The H.P. output will be also . . twice as great, 

The speed now being . . . half as great. 

In a similar way, if — 

The load be made .... one quarter as great, 

K 



130 ELEMENTS OF ELECTRIC TRACTION 

111 order to obtain — 

A torque .'..,. one quarte?' as great, 

The current will be . . . . half as great ; 

J The JET.P. output will also be . . half as great, 

J The speed now being .... twice as great. 

It will be found, just as before, that if the matter be considered 
from a power point of view, the results are again in entire agreement. 

Input. — If the current in any given case be doubled, the 
voltage being constant, the electrical input will be doubled, and 
therefore the horse-power output should also be approximately 
doubled. 

Output. — If with double the current four times the torque is 
obtained, then under these circumstances the load has been increased 
to four times its original value, but with speed reduced to half its 
original value, the horse-power output is only twice its original 
value, thus corresponding with the electrical input. 

Thus, roughly, in a series motor with — 

Twice the H.P., 
Twice the current, but 
Half the speed and 
Four times the torque. 

And, in a similar way — 

Half the U.V., 
Half the current, but 
Twice the speed and 
One quarter the torque. 

This will give an approximate idea as to the variation that 
takes place in a series motor. 

Actually, however, it may be said the magnetic field of an 
ordinary series motor, when under ordinary working conditions, 
will not increase and decrease in strength at the rate indicated 
above, namely, double the current double the magnetic field (the 
magnets approaching more or less the state of saturation), but will 
increase at some lesser rate ; consequently, the speed will not decrease, 
and the torque will not increase at such a rapid rate — that is, as the 
B.H.P. output is increased, or, vice versa, as the B.H.P. output is 
decreased. The more the magnets are saturated (the field in con- 
sequence becoming more or less constant), the less rapid will be this 
rate of variation, and the more will the behaviour of a series motor 
begin to resemble the behaviour of a shunt motor. 

On the other hand, if with reduced load the magnets become 
only slightly magnetized, variations in the current may bring about 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 131 

even a greater rate of variation in the strength of the magnetic field, 
and consequently with reduced current, due to reduced load, a greater 
rate of increase of speed; hence the excessive increase of speed on 
very light loads, and the consequent danger already referred to. 

The results tabulated on p. 132, obtained from a Dick Kerr 
motor, will give some idea as to the results obtained in actual 
practice. The speed is not given in revolutions per minute, but 
the equivalent in miles per hour, as already explained. 

The efficiency, it may be said, is the efficiency per cent., and 
includes gear losses. 

From this data, curves can be plotted, say, with amperes on the 
horizontal line, and efficiency, miles per hour, horse-power, and 
horizontal effort (that is, tractive effort or draw-bar pull) in pounds, 
on the vertical; such curves, if plotted, will show how the various 
quantities vary throughout the whole range given, and in this way 
the complete behaviour of the motor is shown in one diagram. 

These same particulars are shown plotted in this way in Fig. 30, 
page 146. 

From these results, it will be seen that the draw-bar pull increases 
and the speed decreases as the B.H.P. output increases, and vice 
versa, but the rate of increase and decrease is not as rapid as that 
indicated in the rough example taken, for reasons already explained. 

Speed Regulation. — There are two methods by which the speed 
of a motor can readily be varied, that is, within certain limits, and so 
regulated if required — 

1. By varying the field strength, more definitely, by varying the 
current passing through the field coils. 

2. By varying the pressure at the terminals of the motor. 

1. Varying Field. 

Field weakened. — In a general way, if the field strength of a motor 
— pressure of supply and load being constant — be weakened, the speed 
will be increased. 

Field strengthened. — If the field, under similar conditions, be 
strengthened, the speed will be reduced. 

2. Varying Pressure. 

Pressure increased. — In a general way, if the pressure at the 
terminals of a motor be increased — load and field being constant — the 
speed will be increased. 

Pressure reduced. — If the pressure, under similar conditions, be 
reduced, the speed will be reduced. 

The above, of course, assumes that the variations either in the 
field strength, or in the pressure, are suitable ones for the motor under 
consideration. 

The reasons for the above behaviour will now be considered more 
in detail. 



132 



ELEMENTS OF ELECTRIC TRACTION 





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PROPERTIES OF CONTINUOUS-CURRENT MOTORS 133 

Varying Field. — If the field of a motor, which is running under 
a constant load and voltage, be slightly weakened, there will be a 
corresponding slight reduction in the back E.M.F. generated. 

N"ow, a slight decrease in the back E.M.F. means, as already seen 
(see Fig. 29) a much greater proportionate increase in the effective 
E.M.F. With this increase in the effective E.M.F., there will be a 
corresponding increase in the armature current. Consequently, for 
the time being, the armature current will be increased far more in 
proportion than the field has been decreased in strength. The result 
is that, until a readjustment takes place, there will be an increase 
in the torque exerted by the motor, which increase will cause the 
motor to speed up. In speeding up, this increased armature current 
will be gradually reduced in value until the torque exerted by the 
motor again balances that due to the load, etc., the motor then 
running and continuing to run at some uniform, but higher speed. 
The final value of the current passing through the armature, it must 
be noted, will be greater than the original value, the increase in 
value depending upon the extent to which the field has been 
weakened. The reason for this increased current is, that as the load 
has not been decreased, the motor will still have to exert at least 
the same torque, and this, with a weakened field, means an increased 
armature current. 

It should also be noted that with an increase in the current 
there will be an increase in the electrical input, which increased 
input corresponds with the increased output. For, although the 
load has not been increased, the speed has, hence the increased 
H.P. output. 

In a similar way, if the field be slightly strengthened, the effective 
E.M.F. and armature current will be reduced in a greater proportion 
than the held has been strengthened, and there will be, for the time 
being, a consequent reduction in the torque exerted by the motor. 
The motor will slow down, and the decreased value of the current 
and torque will be gradually increased again to suit the resisting 
torque due to the load until balance is again reached, the motor 
finally running at some uniform but reduced speed. 

The motor will finally, under these circumstances, take a less 
current than originally, the reduced input corresponding with the 
reduced output due to the lessened speed. 

If the field of a motor l)ecomes— say due to some accidental cause — 
excessively weakened, one of two things is liable to happen, depending 
upon the value of the load upon the motor. 

If the motor is running under anything like its normal load, an 
excessive armature current will be the outcome of the serious 
weakening of the main field, the motor in this way endeavouring 
to keep its torque equal to that required for the load, etc. If the 



134 ELEMENTS OF ELECTRIC TRACTION 

field is so weak that, despite the excessive current, the torque exerted 
by the motor is unable to cope with the load, the motor will slow 
down and stop. 

The danger here, of course, lies in the excessive current that 
would flow under such circumstances, with the consequent risk of 
l)urning the motor out unless suitably protected. Practically, of 
course, under such circumstances, the fuses or cut-outs, if suitably 
provided, would " blow." 

If the motor, on the other hand, is only very lightly loaded, then, 
under tliese circumstances, the armature will speed up excessively, 
the motor again in this way endeavouring to keep its torque equal 
to that required for the load, and as this is only small, the speed will 
liave to be excessive to cut down the excessive armature current that 
would otherwise flow. 

The danger here lies in the excessive speed, as wdth such increase 
in speed, there would be a corresponding increase in the centrifugal 
force, with the consequent risk of the conductors and commutator bars 
bursting away from the armature core and body, and in this way 
wrecking the motor. 

Extent of Variation in Speed. — To what extent a motor will 
vary its speed with varying field can possibly be most easily seen by 
taking a rough numerical example. An extreme case will be taken 
in order to show more clearly the nature of the variation taking 
place — 

Assume the motor in question to be running with a constant load 
and with a pressure, say, of 100 volts at the terminals of the motor. 
If with the load in question a back E.M.F. of 90 volts were being 
generated, then with an armature resistance of, say J ohm, 20 amps, 
would be passing through the armature. If, now, the field strength 
be decreased, say, until it has only half its original value (this will 
mean, in all probability, much less than half the exciting current), 
the armature current will have to be increased until it has double its 
original value in order that the torque exerted by the motor may 
be the same, this being essential as the load is not reduced, a 
current of 40 amps, with half the original field strength exerting 
the same torque as a current of 20 amps, with the original field 
strength. 

The question now resolves itself into finding what change has 
to take place in the speed in order that 40 amps, may now flow with 
a field reduced in strength to half its original value. For a current 
of 40 amps, to flow, the back E.M.F. will have to be 80 volts. 
Originally, the back E.M.F. was 90 volts, and the speed, say, pro- 
portional to 90. Now, had the field been kept constant, a speed 
proportional to 80 would have been required to generate the back 
E.M.F. of 80 volts which is now required, but with the field reduced 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 135 

in strength to one-half its value, the speed will now have to be double 
this, that is, proportional to 160, in order to generate a back E.M.F. 
of 80 volts. Thus, half the field strength means, roughly, double the 
speed, strictly speaking, somewhat less than double depending upon 
the load. 

It will be seen from above that if the speed had not increased, 
the back E.M.F. would have been reduced to some 45 volts, and the 
effective E.M.F. increased to 55 volts, thus increasing the current to 
5^ times its original value, while the field would only have been 
weakened to one-half its original value. The result would have 
been a torque 2 J times as great as the original torque, thus showing 
the tendency at work which causes the motor to speed up until 
torque balances torque, and speed again becomes uniform at a higher 
value, as shown above, the increase in the input approximately corre- 
sponding to the increased output due to the increased speed. In a 
similar way, to double the strength of the field will approximately 
halve the speed of the motor. 

In shunt or cumulative compound motors a certain amount of 
variation can in tliis way be obtained by having a shunt regulator 
in the shunt circuit. A shunt regulator consists of a set of suitable 
resistances, and a switch, which enables these resistances to be either 
inserted or cut out of the shunt portion of the circuit as desired. 

By this means the current passing through the field coils can be 
varied to a certain extent, and in this way a certain amount of varia- 
tion in the speed obtained. 

In a series motor the field current can only be regulated inde- 
pendently of the armature current, by shunting, or diverting a portion 
of the armature current through some other path than that of the 
field. No attempt is made, however, in the ordinary series parallel 
system as adopted for traction work for regulating the series motors 
in this way. 

It may be said, however, in the Johnson-Lundell regenerative 
system, regulation of this kind is carried out. 

Varying Voltage. — It has been stated that the speed of a motor 
will increase and decrease with increase and decrease of pressure at 
the armature terminals, if field strength and load are kept constant. 

The reason for this will first of all be considered by taking the 
case of a motor with constant excitation, and it will then be seen 
what effect a varying pressure has in the case of a series or a shunt 
motor — 

Motor with Constant Excitation. — A constant field strength can 
readily be obtained by separately exciting the field circuit of a shunt 
motor. A constant pressure of supply therefore across the field 
terminals will mean a constant exciting current, and in consequence, 
apart from demagnetizing actions, a field of constant strength. The 



136 ELEMENTS OF ELECTRIC TRACTION 

pressure across the armature terminals, on the other hand, can be 
varied without in any way interfering with the field. 

If, then, a motor so arranged be ran with a constant load, it will 
have to exert in consequence a constant torque, and this with a field of 
constant strength will mean also an armature current of constant value. 

Therefore, in such a motor the armature current will simply de- 
pend upon the load, and, practically speaking, whatever be the voltage 
applied, as long as the load is constant, the armature current will be 
constant, the voltage affecting simply the speed, the reason being as 
follows : — 

The motor, with a given voltage and load, will run at some uniform 
speed, and in so doing will generate a certain definite back E.M.F. 
If now the voltage be increased, a greater current will tend to flow, 
and a greater torque will for the time being be exerted. The motor 
will speed up, in consequence increasing its back E.M.F. until the 
armature current becomes again reduced to its original value, the 
motor then exerting the same torque, but running at some higher, 
and with the torques balancing one another, at some uniform speed, 
corresponding to the increased voltage. 

Thus an increased pressure will bring about an increase in the 
speed, and in a similar manner a decrease in the pressure will bring 
about a decrease in the speed. 

Extent of Variation in Speed. — The extent to which the speed 
will vary with varying pressure will now be considered. 

Taking the same figures as were employed in dealing with varying 
field strength, if the original pressure were 100 volts, then, with a 
back E.M.F. of 90 volts and an armature resistance of J ohm, 20 
amps, would be flowing through the armature. 

If now the voltage at the armature terminals be doubled, the 
back E.M.F., it will be seen, will now have to be 190 volts in order 
that the same current of 20 amps, may flow, and in order that the 
torque exerted may be the same. 

Thus the back E.M.F. has had to be slightly more than doubled, 
and this with a field of constant strength means that the speed must 
also be slightly more than doubled. 

Consequently, a motor with a constant field strength and constant 
load, will, with double the voltage, have approximately double the 
speed, and with half the voltage half the speed, the armature current 
remaining practically constant. 

Strictly speaking, with double the voltage, slightly more than 
double the speed, and with half the voltage, slightly less than half 
the speed, depending upon the value of the load, the lighter the 
load the less being the difference. 

Series Motor. — With constant load and therefore constant torqtie, 
it will readily be seen that no variation will have to take place in 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 137 

the armature current, as any alteration in the value of the armature 
current will cause the torque exerted to vary, not only due to the 
variation in the current itself, but also due to the consequent varia- 
tion which would take place in the field strength. Consequently, 
in a series motor, as long as the load is constant the armature current 
will be practically constant, and is in this way independent of the 
voltage applied and the consequent speed the motor may run at. In 
fact, just as in the previous case of the separately excited motor, the 
armature current will simply depend upon the load. Practically 
speaking, whatever be the voltage applied to a series motor, as long 
as the load is constant the armature current will be constant, the 
voltage affecting simply the speed. 

The series motor, therefore, with a constant load will behave with 
a varying voltage in a similar manner to that of a motor with field of 
constant strength, such as has just been considered. Consequently, a 
series motor with double the voltage will slightly more than double 
its speed, and with half the voltage will have slightly less than half 
the speed, depending upon the value of the load. 

Shunt Motor. — If the voltag^e across the terminals of a shunt motor 
be increased, it will be noticed that while the motor will tend to 
increase its speed due to the increased pressure across the terminals, 
there will also be an increase in the current passing through the 
field coils, and hence an increase in the field strength at the same 
time, which increase will tend to reduce the speed. The action, 
however, of the field will depend upon the degree of saturation of 
the field magnets. Under most ordinary working conditions, as 
the field magnets would be more or less saturated, a reasonable 
increase and decrease in the terminal voltage would bring about an 
increase or decrease in speed, but not to the same extent were the 
field absolutely constant. 

In all shunt motors, and motors employing a shunt winding, it is 
essential that the field circuit be made first, before completing the 
main armature circuit. If this were not done, the motor on light loads 
with only its residual field might speed up excessively while on 
heavy loads, a sufficient torque would not be available to start the 
motor up, and an excessive current would in consequence flow. 

On the other hand, quite apart from any other considerations, the 
shunt circuit should never be broken suddenly, as the sudden dying 
down of the magnetic lines which thread through the core, as it were, 
cutting the great number of turns of wire, would generate or induce 
a very large E.M.F. many times the normal, and this E.M.F. might 
be sufficiently great to actually pierce and so break down the insula- 
tion. Special devices are generally adopted when shunt circuits of 
any size have to be broken. Windings of any description which 
produce similar effects are generally termed " inductive windings." 



138 ELEMENTS OF ELECTRIC TRACTION 

Compound Characteristics. — The characteristic properties of 
the compound motor will now be considered a little more in detail — 

Cumulative Compound Motor. — On very light loads the excitation 
due to the series winding will be very small, as the armature current 
will be small. The field, however, due to the shunt excitation will 
prevent the motor gaining an excessive speed ; in fact, under these 
conditions its behaviour will resemble very much that of a shunt 
motor. As the load is increased and the amperes increase, the 
field will be increased in strength, and consequently the speed will 
drop. There will be a greater drop of speed than in an ordinary 
shunt motor due to this increase of field strength, but there will also 
be an increase in the value of the torque exerted over and above 
that of a shunt motor of similar construction. 

The amount of this speed and torque variation will depend upon 
the extent to which the machine has been compounded 

The advantage of such a motor is that on heavy loads it has some 
of the advantages of the series motor without the corresponding 
danger of the excessive speeds on lighter loads. 

Differential Compound Motor. — This motor, as already explained, 
can be designed for constant speed; the series winding, being in 
opposition to the shunt, weakens the field on heavy loads, thus 
automatically increasing the speed, which would otherwise tend to 
drop. The danger with this type of motor is that, on very heavy over- 
loads, the field will be so considerably weakened that the torque will 
not be great enough to overcome the resistance of the load ; the motor 
will thus stop, and an excessive current will flow, thus damaging the 
motor unless suitably protected by means of fuses or cut-outs. 

Losses. — Up to the present the various losses which take place 
in a motor have only been referred to in a general way. These 
losses will now be considered more in detail. 

They consist of — 

(1) Certain losses which occur in the copper windings, and are, 
in consequence, often called the " copper " losses. 

(2) Certain losses which occur chiefly in the iron portion of the 
armature, and are, in consequence, often called the " iron " losses. 

(3) The various frictional losses. 

Copper Losses. — These might also be termed the "electrical" 
losses, as a certain amount of the electrical energy supplied to a 
motor never becomes converted into mechanical energy, but is trans- 
formed directly into heat energy. This is due to the fact that the 
armature and field windings possess a certain resistance, and conse- 
quently energy has to be spent in simply driving current through 
these windings. 

The greater tlie resistance, or the greater tlie current, the greater 
the energy lost. 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 139 

In the small series motor referred to in Chapter VI., the resist- 
ance of the armature and field windings was seen to be, roughly, 
1^ ohms. To send the full-load current of 15 amps, through this 
resistance will require a pressure of 22^ volts. Consequently, when 
this particular motor is running on full load, energy is expended 
at the rate of 22 J x 15, namely, 337*5 watts, or, very roughly, 
at the rate of 0'4 H.P., in driving simply the full-load current 
through the windings, and the energy so expended is converted into 
heat. 

On full load the electrical power supplied to the motor is, 
roughly, about 2 E.H.P., 15 amps. X 100 volts being equal to 
1500 watts, or, strictly, 2-01 E.H.P. 

Consequently, it will be seen that out of the total electrical 
power supplied to this particular motor at full load, electrical energy 
at the rate of some 0'4 H.P. is not converted into mechanical energy. 

Another rule for obtaining the watts lost in any given resistance 
is to multiply the value of the resistance in ohms by the square of 
the current in amperes. Thus — 

IJ X 15 X 15 = 337-5 watts 

This is generally written — 

C^R = watts 

where C represents the current in amperes, 
R „ „ resistance in ohms. 

These losses are sometimes, in consequence, called the C^R 
losses. 

It must be noted that in a shunt motor the losses occurring in 
the armature have to be calculated quite separately from those of 
the field, as the current passing through the field is only a small 
fraction of the current passing through the armature, the field 
winding again having a much higher resistance than the armature. 

The resistance of the armature and field winding in the small 
series motor just considered is fairly high, and the copper losses also 
fairly high in consequence. 

In an ordinary series motor, such as is used in tramway work, 
the copper losses will possibly amount on full load to some 10 per 
cent, or so of the total power supplied. Consequently, some 10 per 
cent, of the total power supplied on full load will not be converted 
into mechanical energy. 

The total electrical energy transformed into mechanical energy 
will not all be available for useful purposes, a certain amount of 
energy being lost, as far as useful purposes are concerned, in the 



140 ELEMENTS OF ELECTRIC TRACTION 

iron portion of tlie armature, and a -certain amount of energy being 
required to overcome the various frictional resisting forces. 

Iron Losses.— The losses occurring in the iron portion of the 
armature are due to two causes ; one due to the retentivity of the 
iron or steel employed, whicli is termed the " hysteresis " loss, and 
the other due to certain idle currents which are set up in the core, 
termed the *' eddy-current " loss. 

Hysteresis Loss. — Owing to current circulating round the arma- 
ture core, the iron core becomes magnetized. As the mau;netizino- 
action due to these currents is always constant as regards direction, 
and the armature revolves, the portion that has north polarity at 
one moment becomes magnetized with the opposite polarity every 
half-revolution in the case of a simple two-pole machine. 

Rapidly reversing the magnetism in a piece of iron or steel, as 
seen in Chapter II., produces a certain amount of heat — depending, 
among other things, upon the retentivity of the iron or steel. Energy 
has to be expended to force this reversal of magnetism upon the iron, 
the energy being converted into heat ; and, in consequence, the energy 
so expended, as far as useful purposes are concerned, is lost. To 
lessen this loss as much as possible, the armature is generally built 
np of either charcoal or a special make of soft steel sheets, which, 
having a low retentivity, reduces this loss. This loss will depend not 
only on the degree of saturation of the armature core, but also upon 
the speed. 

Eddy -current Loss. — Just as currents are set up in the moving 
conductors of a dynamo when the circuit is complete, so, in a similar 
w^ay, an electromotive force is generated, tending to send currents 
circulating down one side and up the other of the armature core, 
seeing it is constructed of a conducting material, namely, iron, and 
that there is a complete circuit in the core itself. These currents 
are called " eddy currents," and hence the loss due to this cause is 
termed the " eddy-current " loss. 

As energy here again has to be expended in order to generate 
these currents, the energy so expended, being transformed into heat, 
is lost as far as all useful purposes are concerned. To lessen this 
loss as much as possible, the core is built up, as already explained, of 
thin sheets, which are insulated from one another, thus breaking the 
circuit, as it were. 

These losses increase with increase of speed, and, together with 
the losses due to magnetic hysteresis, make up the total iron losses. 

In an ordinary traction motor, the total iron losses on full load 
will possibly amount to some 3 or 4 per cent, of the total energy 
supplied. 

Frictional Losses. — These consist of — 

The friction of the shaft in its hearings. In a tramway motor the 



PROPERTIES OF CONTINUOUS-CURRENT MOTORS 141 

friction of gearing and bearings connected witli it is generally in- 
cluded in giving results of tests ; these frictional losses, it may be 
said, will increase with load, owing to the increased pressure on the 
bearings. 

The friction of the hricshes on the commutator. The friction due 
to these will be small and practically constant. 

The friction due to the resistance of the air ; "windage," as it is 
generally called. The friction due to this increases as the speed 
increases. 

In an ordinary tramway motor the total frictional loss on full 
load, including gearing, will possibly amount to some 5 per cent, of 
the total power supplied. 

Mechanical Energy available. — In conclusion, it will now be 
seen that a certain portion of the total electrical energy supplied is 
never converted into mechanical energy, and again, that portion that 
is converted is not all available for use. It should be remembered, 
however, that the total loss due to all causes in well-designed 
dynamos or motors is not very great; in tramway motors some 15 
to 20 per cent, being the total loss at full load, including gear 
losses, etc. 

From the above it will be seen that if the current in amperes 
circulating through the motor be multiplied by the voltage of supply, 
the product will be equal to the watts supplied, and if from this be 
deducted the copper losses expressed as so many watts, the result 
will give the rate at which electrical energy is being converted into 
mechanical energy, expressed as so many watts. This, it may be 
said, is equal to the current in amperes circulating, multiplied by the 
value of the back E.M.F. in volts. 

If, now, the above number expressing the watts be divided by 
746, the result will give the rate at which electrical energy is being 
converted into mechanical, expressed as so much H.P. 

The value of the B.H.P. will be less than this, as a certain 
amount of power will be expended in overcoming the resisting forces 
set up, and due to magnetic hysteresis, eddy currents, and the various 
frictional resisting forces. 

In a similar way, the nett torque the motor exerts will be less 
than the actual torque exerted by the motor, as a torque will be 
required to overcome the resisting forces set up and due to the 
above-mentioned causes. 

Secondary Actions. — It can now be seen what affects some of 
the secondary actions that have been referred to have on the speed of 
a motor. 

Demagnetizing Effects. — Owing to the magnetizing effect pro- 
duced by the current circulating round the armature core, certain 
demagnetizing actions are set up in the motor, just as in the dynamo ; 



142 ELEMENTS OF ELECTRIC TRACTION 

these demagnetizing actions tend to weaken the main field, and the 
greater the current the greater will this weakening effect be. From 
what has already been said, it will now be seen that such demag- 
netizing effects will tend to increase somewhat the speed of the 
motor, depending, of course, upon the value of the demagnetizing 
force, and the strength of the field. 

Drop in Pressure. — Any drop in pressure that may take place at 
the terminals of the motor will tend to reduce the speed. The drop 
in pressure will depend not only on the current flowing, but also upon 
the size and length of cables conveying the current. 

Friction. — Any increase in any one of the frictional resisting 
forces will virtually be an increase of load, and will therefore tend to 
reduce the speed. 

Hysteresis and Eddy Currents. — As these increase with increase of 
speed, they will virtually increase the load on the motor with increase 
of speed, and in this way tend to reduce its speed. 

From the above it will be seen that, while with increase of load 
the speed will tend to decrease, owing to increased friction in bearings 
and drop in pressure at terminals, the speed will also tend to increase, 
due to the greater demagnetizing effects produced by the increased 
current. 

In conclusion, it may be stated that the heating and sparking 
effects are the two main limiting factors which determine the maximum 
load that can be put upon a motor. 

With very heavy loads, and in consequence very heavy currents, 
the armature and field windings will heat up, and the consequent 
rise in temperature if such overload be kept on for any length of 
time may finally be sufficiently great to damage and break down the 
insulation. Also, with heavy loads and the consequent increased 
currents, further difficulty will be experienced with sparking at the 
commutator. 



CHAPTER IX 
APPLICATION OF MOTORS TO TRACTION 

In dealing with the application of motors to traction, the following 
principles in connection with draw-bar pull — which have already been 
considered in detail — should be clearly borne in mind : — 

Draw-bar Pull. — The horizontal effort or draw-bar pull exerted 
by a given motor fitted to a car, with a given ratio of gear wheels 
and a given diameter of car wheels, will primarily depend upon — 
strength of field and the value of the armature current. 

In other words, the draw-bar pull will vary with varying values 
of either of the above quantities, or a suitable variation of 
both. 

In an ordinary series motor, where the same current passes through 
both armature and field, the draw-bar pull will simply vary with 
varying values of the armature current. 

Consequently, when series motors are employed for traction work, 
with a given value of current there will be a given value of the draw- 
bar pull, and an increase or decrease in the draw-bar pull can only 
be brought about by a corresponding increase or decrease in the value 
of the current passing through the motors. 

If two motors are employed, the total draw-bar pull will be 
twice that exerted by one, provided both are doing their equal share 
of work. 

In traction work the draw-bar pull is required in order to over- 
come — 

(1) Frictional resistance, amounting under average tramway con- 
ditions to some 25 to 30 lbs. per ton weight of car and passengers. 

(2) Gravitational pull when the car is mounting a gradient. 

The numerical value of this in pounds for any particular gradient 
is obtained by dividing the total weight of car, etc., in pounds, by the 
length in feet the car travels on this particular gradient in rising a 
vertical height of 1 foot. 

(3) Inertia of the car, resisting acceleration. 

102*6 lbs. per ton of total weight is required to give an accelera- 
tion of 1 mile per hour per second, 154 lbs. per ton being required to 
give an acceleration of 1 J miles per hour per second. 



144 ELEMENTS OF ELECTRIC TRACTION 

Any force exerted over and above that required for overcoming 
frictional resistance, if the car is on the level, or frictional resistance 
and gravitational pull, if the car is on a gradient, will be available 
for accelerating purposes. 

When a car is being accelerated, it must be remembered that the 
armatures of the motors are also being accelerated, and in this way, 
by an increase of back E.M.F. and reduction of current, the accele- 
rating force, after all starting resistance has been cut out, is gradually 
reduced, until the draw-bar pull just balances the frictional resistance 
if the car is on the level, or just balances frictional resistance and 
gravitational pull if the car is on a gradient. Acceleration then 
ceases, the car then travelling, and the motors rotating, at some 
uniform speed. 

Thus the motors always tend to reduce the value of the 
accelerating force, until finally all accelerating effort ceases. 

Consequently, when a car is travelling at a uniform speed, 
frictional resistance and gravitational pull are the only loads the 
motors have. An increase or decrease in the value of either the 
friction or the gradient, with a car of given weight, will bring 
about an increase or decrease in the load upon the motors, with a 
corresponding increase or decrease in the value of the draw-bar pull 
that has to be exerted. 

Varying Value of the Draw-bar Pull. — It will readily be seen 
that, under ordinary conditions, the value of the draw-bar pull when 
the car is being accelerated will be considerably in excess of that 
required simply to maintain the car at any given speed under the 
same conditions. 

Thus, with a 10-ton car and a tractive resistance of 25 lbs. per 
ton — 

To give an acceleration of 1 J miles per hour per second on the 
level would require a draw-bar pull of 1540 -f- 250, or 

1790 lbs. 

To simply maintain a reasonable speed on the level would, on 
the other hand, only require a draw-bar pull of . 250 lbs. 

To give an acceleration of 1^ miles per hour per second to a 
car mounting a gradient of 1 in 20 would require a draw-bar 
pull of 1540 + 250 4- 1120, namely .... 2910 lbs. 

To simply maintain a reasonable speed on such a gradient would 
only require a draw-bar pull of 250 + 1120, or . 1370 lbs. 

To give an acceleration of li miles per hour per second to a 
car mounting a gradient of 1 in 10 would require a draw-bar 
pull of 1540 -f- 250 -f 2240, namely 4030 lbs. 

To simply maintain a reasonable speed on such a gradient would 
only require a draw-bar pull of 250 + 2240, or . 2490 lbs. 



APPLICATION OF MOTORS TO TRACTION 145 

Type of Motor. — From this it will be seen that whatever type 
of motor be adopted, it will have to be capable of exerting for short 
periods — that is, when starting and accelerating — a draw-bar pull 
considerably in excess of that required simply to maintain a given 
speed, under the same conditions of load and gradient. 

Up to the present the series motor has been largely adopted for 
traction work. One of the advantages claimed for this type of motor 
liitherto has been that a greater torque, and hence a greater draw-bar 
pull, could be obtained with this type of motor with a given current 
than with a shunt motor of the same size and weight. It is doubtful, 
however, if such a contention could now be held, in view of the results 
recently obtained by Mr. Eaworth with the particular type of shunt 
motor that he has employed in his regenerative system. 

One advantage the series motor has, is that no serious danger 
exists in the event of the circuit being broken either at the trolley or 
the rails. In a shunt motor, as already pointed out, an excessive 
rise of pressure is liable to take place in the event of the field circuit 
being broken, the rise of pressure in some cases being sufficiently 
great to pierce, and so break down, the insulation of the field windings. 
It should be added, however, that Mr. Eaworth claims to have over- 
come this and other difficulties which have arisen in connection with 
the use of shunt motors for traction work. 

At the present time it is, however, a debatable point amongst 
engineers as to which is the more suitable motor for traction work, 
the series or the shunt, especially having in view "regeneration." 
No attempt will, however, be made here to discuss this question. 
At the present time two regenerative systems are being put forward, 
in one of which shunt motors are employed, and in the other, series 
motors. These two systems are rival ones, and time and experience 
will probably alone decide the issue. 

It may, however, be just pointed out that the problem consists 
not only in considering the relative merits of two different types of 
motors, but also in considering the nature of the service demanded, 
not forgetting that capital cost, general efficiency, running expenses, 
renewals, wear and tear, and, last but not least, public safety, are all 
factors which complicate the problem, and which must all have their 
due consideration. 

Series Motors as applied to Traction 'Work. — The series 
motor as applied to traction work will now be briefly considered. 
In the previous chapter, certain results obtained from actual tests of 
a Dick-Kerr series motor were given in tabular form. These same 
results are now shown plotted in diagram form. See Fig. 30. 

This particular size of motor, as will be seen from the diagram, 
is capable of giving out 28 B.H.P., with 500 volts pressure, without 
the windings increasing their temperature more than 75° C. or 135° F, 

L 



146 



ELEMENTS OF ELECTRIC TRACTION 



above that of the surrounding air, after one hour's run with this 
particular output. 

The rise of temperature given is the usual one at which traction 





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APPLICATION OF MOTORS TO TRACTION 147 



motors are generally rated, as far us the H.P. is concerned, as 
previously explained. 

If, now, the diagram be carefully studied, it will be seen that 
when the motor is running at a certain definite speed, it will 
be taking a given number of amperes, exerting a certain definite 
D.B. pull, and giving a certain definite B.H.P. output. All these 
quantities are definitely connected, and ho alteration can take place 
in the speed, for instance — unless some means of regulation be 
adopted — without a corresponding alteration taking place in each of 
the above quantities. 

Thus, if the above motor were fitted to a car with the particular 
gear ratio of 5*07 to 1, and car wheels 30 inches diameter as given, 
the following results would be obtained if the motor was supplied 
with pressure at 500 volts : — 

When the car is running under such conditions, that it has, say, a 
uniform speed of 8 miles per hour, the motor at that speed will be 
taking 65 amps., and will be exerting a D.B. pull of 1570 lbs., the 
output in such a case being 33^ B.H.P. 

Or, again, when the car is running under such conditions that it 
has, say, a uniform speed of 16 miles per hour, the motor at this 
speed will be taking 20 amps., and will be exerting a D.B. pull of 
240 lbs., the output now being 10 B.H.P. 

The following table gives the approximate values of current, 
draw-bar pull, and B.H.P. that will be obtained with the above motor 
with the following variations of speed : — 



Speed in miles per hour 


8 


10 


12 


14 


16 


18 


20 


201 


Current in amperes 


Qb 


42 


30 


24 


20 


17 


15 


141 


D.B. pull in pounds 


1570 


850 


500 


340 


240 


180 


140 


125 


B.H.P 


33^ 


221 


16 


121 


10 


H 


7 


6-8 



On studying the above figures, it will be seen — 

(1) That the draw-bar pull increases rapidly in value with 
increase of current. 

(2) That there is a definite value of the draw-bar pull for each 
definite speed, and that the draw-bar pull decreases in value with 
increase of speed. 

These characteristics will now be considered — 

(1) Rapid Increase of Draw-bar Pull with Increase of 
Current. — The draw-bar pull, depending as it does in any given 
case both upon strength of field and armature current, increases 



148 ELEMENTS OF ELECTRIC TRACTION 

rapidly in value with increase of current, because an increase in 
current — within certain limits — means also an increase in field 
strength. 

The rapid increase of draw-bar pull with increase of current 
must not, however, lead to any confusion with regard to the actual 
draw-bar pull exerted under any given conditions. 

The draw-bar pull exerted in any given case simply depends 
upon strength of field and armature current, and hence, as far as the 
field itself is concerned, simply upon its actual value, and not upon 
how quickly this particular value of field strength has been reached, 
nor upon the means whereby this particular field strength has been 
obtained. 

Again, with a given size of field magnets, that is, with a motor, 
of given dimensions, it must be remembered there is a limit to the 
number of magnetic lines which can be forced through the magnet 
cores, this limit being reached when the magnets become practically 
saturated. Consequently, when saturation is reached, this rapid, 
increase of draw-bar pull with increase of current will cease. 

Here, again, maximum draw-bar pull with a given size of magnet 
cores will depend simply, as far as the field itself is concerned, upon 
the maximum number of lines which can be forced through them, 
and not upon the means adopted in order to get this degree of 
saturation. This must be clearly borne in mind in considering the 
relative torques or draw-bar pulls exerted by shunt and series 
motors. Therefore, with a given field strength and a given armature 
current, there will be a given draw-bar pull, quite independent as to 
whether this particular field strength is brought about by shunt or 
series windings. 

(2) Definite Draw-bar Pull with Definite Speed. — In the 
first place, it must be noted that the speeds given are those which 
would be obtained if the motor were supplied with a pressure of 
500 volts across its terminals. Hence these speeds are on the 
understanding that all starting resistance has been cut out of 
circuit ; the motor then having the full pressure across its terminals. 

The effect of inserting starting resistance, it may be added, can 
be looked at in two ways. 

From one point of view, the inserting of starting resistance can 
be looked upon as simply increasing the total resistance of the 
circuit, and in this way the current passing through the motor is 
reduced to less than it otherwise would be. 

From the other point of view, as a certain pressure is required to 
drive whatever current is flowing through the resistance itself, a less 
pressure than the pressure of supply will be available to drive 
current through the motor. From this point of view, the inserting 
of resistance into the circuit reduces the pressure across the 



APPLICATION OF MOTORS TO TRACTION 149 

terminals of the motor. The reduced pressure, of course, brings 
about, as far as the current is simply concerned, the same result as 
before, namely, a current of less value than it otherwise would be. 

Reducing the pressure across the terminals of a series motor, on 
the other hand, has, as already seen, the effect of reducing the speed. 

Consequently, in studying the above diagram, it must be 
remembered that all the results are such as would be obtained 
when all starting resistance is cut out and the motor has the full 
pressure of 500 volts across its terminals. 

Thus, with 500 volts pressure across the' motor terminals, the 
motor will exert, when running at a speed of 8 miles an hour, a draw- 
bar pull of 1570 lbs. The motor may not continue running at this 
speed, in which case the draw-bar pull will not continue to have the 
value of 1570 lbs., but it may continue to speed up until finally a 
uniform but higher speed is obtained, with a corresponding decreased 
value of the draw-bar pull. Whether the speed, however, of 8 miles 
an hour be a uniform one, or only its instantaneous value, it must 
be noted that the draw-bar pull at that speed will be 1570 lbs. when 
the motor has 500 volts across its terminals. 

Now, the practical outcome of a different draw-bar pull for each 
different speed is as follows : — 

As a much greater draw-bar pull is required to maintain a car at 
a reasonable uniform speed on a gradient than that required to 
maintain the same car with the same tractive resistance at a uniform 
speed on the level, the speed on a gradient will be different from 
that obtained on the level, and the fact that the speed increases as 
the draw-bar pull decreases, indicates that the speed that will be 
finally attained on the level will be greater than that finally attained 
on a gradient. The greater the gradient, the greater within certain 
limits will this difference in speeds be. In fact, with a constant 
voltage across the motor terminals, the uniform speed obtained on one 
gradient will be different from that obtained on a gradient of another 
value, and the speed on either of these will be different again from 
that obtained on the level. 

To put the matter into another form, the maximum speed that 
can be obtained, say with a given motor and a given car on any 
one gradient, will be different from that obtained on a gradient of 
another value, and that again different from the maximum speed 
that can be obtained on the level. 

Thus, if two such motors as the one of which particulars 
have been given were fitted to a 10-ton car, the following are 
approximately the maximum speeds which would be obtained on 
the gradients given, assuming a tractive resistance of 25 lbs. per ton, 
and that a pressure of 500 volts was across the terminals of each 
motor : — • 



ISO 



ELEMENTS OF ELECTRIC TRACTION 



Speed 


8 


10 


12 


14 


16 


18 


20 


201 


Total D.B.P. 


3140 


1700 


1000 


680 


480 


360 


280 


250 


D.B.P.due to one motor 


1570 


850 


500 


340 


240 


180 


140 


125 


Gradient 


i 


1 

15 


3\) 


52 


97 


203 


7h 


level 


Current through each 


















motor 


65 


42 


30 


24 


20 


17 


15 


141 


Total B.H.P. 


67 


45 


32 


25 


20 


17 


14 


13-6 



Thus it will be seen in the above case that, while on a gradient of 
1 in 8 a maximum speed of 8 miles per hour can be reached, on the 
level the maximum speed will be considerably greater, namely, just 
over 20 miles an hour. 

Stated in another way, the speed and power of a series motor 
are definitely connected. Now, the power required to maintain a 
car, say, at a speed of 8 miles per hour on a gradient, is more than 
that required to maintain the same car at a speed of 8 miles per 
hour on the level. If the power exerted at a speed of 8 miles per 
hour is just able to maintain that speed on a gradient of, say, 1 in 
8, then on the level it will more than maintain it— in short, the car 
will not continue to run at 8 miles an hour, but will be accelerated 
to some much higher speed until the corresponding power exerted 
by the motor is just equal to that required. 

In the above example, for instance, as already seen, a maximum 
speed of 20^ miles an hour would be reached, the 13*6 B.H.P. then 
exerted being the amount just required to maintain the above car on 
the level at a speed of 20^ miles per hour, with a tractive resistance 
of 25 lbs. per ton. 

Uniform speed on varying values of gradient cannot, therefore, be 
maintained with a series motor unless some means of regulation be 
adopted. This, of course, is only the natural outcome, as a series 
motor with varying load is, as already seen, a variable- speed motor, 
and the load upon a traction motor when a uniform speed is being 
maintained simply varies with weight of car, gradient, and tractive 
resistance. Therefore, with a given weight of car and a given tractive 
resistance, when not accelerating, the load upon the motor will simply 
vary with the gradient. 

Therefore it will be seen, if series motors be fitted to a car, and no 
means of speed regulation be adopted, the pressure of supply also 
being constant, the speed on the level may reach a value far beyond 
that which may be required, and also the speed on a steep gradient 
will be correspondingly and considerably less. The maximum speeds 
here referred to are the speeds, of course, which would be attained 
were the motor allowed to settle down to uniform conditions. 



APPLICATION OF MOTORS TO TRACTION 151 

During the time a car is being accelerated, the speed will depend, 
not only upon the accelerating force at work, but also upon the length 
of time the accelerating force has been at work. 

A shunt motor, by way of comparison, under similar conditions, 
that is, when no attempt is made at speed regulation, will have 
practically one uniform maximum speed under all conditions of load, 
that is, whether mounting a gradient or running on the level. This, 
of course, again being the natural outcome, as a shunt motor is 
practically a constant-speed motor at all reasonable loads. Whether 
the speed were a high or a low one would of course depend upon 
w^hat speed the shunt motor had been designed for with the particular 
voltage of supply. 

The method adopted in tramway traction work for regulating 
series motors will now be considered. 

Series-Parallel Control as applied to Series Motors. — In 
the ordinary tramway system, each car is generally fitted with two 
motors, and these are generally arranged for what is known as series- 
parallel control. 

This arrangement is such that by means of the controller the two 
motors can be placed either in series with one another, or if desired, 
after being placed in series, they can be placed in parallel with one 
another. 

Series. — When the two motors are placed in series with one 
another, whatever current passes through the one motor will also 
pass through the other. In this case each motor will only have half 
the trolley pressure across its terminals, that is, after all starting 
resistance has been cut out. Thus, with 500 volts trolley pressure, 
each motor when in full series will have approximately 250 volts 
across its terminals. 

Parallel. — When the two motors are placed in parallel with one 
another, each motor will have, when all starting resistance has been 
cut out, that is, when on full parallel, the full-trolley pressure, 
namely, 500 volts across its terminals. 

Thus, as far as speed regulation is concerned, it will be seen that 
this is obtained by varying voltage. As applied to two motors, series- 
parallel control thus enables two pressures to be applied to the motor 
terminals, one being the full-trolley pressure, and the other half the 
full-trolley pressure. 

Now, with half the pressure across the terminals of the series motors 
they will have approximately half the speed, that is, with a given load. 

Consequently, when exerting a given draw-bar pull, the motors 
when in full series \vill have approximately half the speed which 
they will have when exerting the same draw-bar pull in full parallel. 

It must, however, be borne in mind, as already mentioned, that the 
series motor is a variable-speed motor, and consequently the speed 



152 



ELEMENTS OF ELECTRIC TRACTION 



the car will finally attain and maintain will also depend upon the 
load upon the motors ; that is, with a car of given weight and a 
given tractive resistance, the uniform speed finally attained will 
depend not only upon the pressure across the terminals of the 
motors, but also upon the value of the gradient the car is 



runnmg on. 



Therefore, whether the motors are in series or in parallel, a car's 
speed will vary with the varying values of the draw-bar pull. 

AVith a car of given weight and a given tractive resistance, this 
will simply mean that the speed a car will attain will vary with 
varying gradients. In fact, just as before, on full series the speed 
obtained on the level will be greater than the speed that can be 
obtained on a gradient. 

Also, in a similar way, variation will take place on full parallel, 
the only difference being that in this case the speeds will be higher. 

It will be seen from this that with this system applied in this 
way it is not possible to obtain any desired speed. The choice a 
driver has under any one set of conditions is simply that of two 
speeds, one being approximately half that of the other. In this way 
the speed on full parallel on a gradient may only just be equal to 
that obtained on full series on the level. 

The following table shows the approximate speeds which would 
be finally obtained on full series and on full parallel with the two 28 
B.H.P. motors fitted to a 10-ton car, with the particular gear ratio and 
diameter of car wheels as previously given, the trolley pressure being 
500 volts, and the tractive resistance assumed to be 25 lbs. per ton : — 



Speed in full series . . . 


4 


5 


6 


7 


8 


9 


10 


lOi 


Speed in full parallel 


8 


10 


12 


14 


16 


18 


20 


201 


Amperes passing 


















through each motor 


65 


42 


30 


24 


20 


17 


15 


14^ 


Total draw-bar pull . . . 


3140 


1700 


1000 


680 


480 


360 


280 


250 


Amperes passing down 
the trolley when 
motors are in series 


65 


42 


30 


24 


20 


17 


15 


^^ 


Amperes passing down 
the trolley when mo- 
tors are in parallel 


130 


84 


GO 


48 


40 


34 


30 


29 


Total B.H.P. when 


















motors are in series 


33^ 


221 


16 


121 


10 


8i 


7 


6-8 


Total B.H.P. when mo- 


















tors are in parallel 


67 


45 


32 


25 


20 


17 


14 


13-6 


Gradient 


1 


1 


1 
3 


.1^ 


1 

i>7 


1 

'J .s 


1 

7 4(> 


level 



APPLICATION OF MOTORS TO TRACTION 153 

On studying the above figures it will also be seen that the draw- 
bar pull exerted by the two motors in parallel is much greater than 
that exerted by the two motors in series, if the speed is the same in 
•each case. 

Additional Speed Regulation. — In some forms of controllers, 
it may be mentioned, such as the K2 (B.T.H.), additional speed 
regulation is obtained after moving on to full parallel by varying the 
field strength, this in turn being obtained by shunting a portion of 
the armature current so that the whole of it does not go through the 
series winding, thus weakening the field and so increasing the speed. 
These notches can be used for fast running on the level, but as 
■weakening the field reduces the torque, armature current remaining 
the same, these notches are not intended for use where a large draw- 
bar pull is required. 

A car fitted with two series motors and arranged for series- 
parallel control is sometimes said to be a two-speed car ; strictly 
speaking, there are two running notches, the full series and the full 
parallel. It is a matter of opinion as to whether this meets the 
whole of the needs of any given system. In many cases it may be 
found that the full series is far too slow, in which case the full-series 
notch simply develops into a mere speeding-up notch, the driver 
practically never halting on it, and so seldom using it as a permanent 
running notch. On the other hand, in many cases the full parallel is 
too fast, the driver in this case simply regulating the speed by 
shutting off and coasting. 

It is a matter of interest to note that in the two regenerative 
systems already mentioned, and which are now being brought forward, 
greater speed variation is given to the driver — in short, more running 
notches. 

Current Economy. — One of the advantages of the series-parallel 
•system is, that when the motors are in series, the same draw-bar pull 
is obtained as would be obtained with double the current with the 
motors in parallel. For example, if 65 amps, are passing down the 
trolley when the motors are in series, each motor will have passing 
through it a current of 65 amps. ; now, to get the same draw-bar 
pull when the motors are put in parallel, 65 amps, would have to 
pass through each motor, just the same as before, and this means that 
a total current of 130 amps, would be passing down the trolley, or 
a current of just double the previous value. Thus, quite apart from 
the type of motor employed with the series-parallel system, not only 
is the series speed more adapted for starting purposes, but a more 
economical use is thus made of the current at starting. 

In the table just given, the various values of current and B.H.P. 
are given for the different conditions, and these should be carefully 
studied. 



154 ELEMENTS OF ELECTRIC TRACTION 

It should, however, be borne in mind that if the motors were put 
into parallel at the start, unless the wheels slipped an excessive current 
would flow, " blowing " the canopy cut-out, as the motors would not 
speed up sufficiently quickly to enable the requisite back E.M.F. to 
be generated. This excessive current would produce, for the time 
being of course, an excessive draw-bar pull — the resistance provided 
being insufficient of itself to keep the current within reasonable 
limits — but a time would elapse before the car could sufficiently 
respond, and in the mean time the cut-out would in all probability 
" blow." 

The above, however, shows that with a given current passing 
down the trolley, a greater starting effort can be obtained with the 
motors in series than with the motors in parallel. 

Controllers. — The controller is that portion of a car's equipment 
which enables all the operations in connection with the regulation 
of the motors to be performed in their proper order. It may be 
described as a somewhat complicated switch, by the operation of 
which the necessary and various connections can be made. 

There are various types and makes of controllers now in use. 
No attempt will be made here to describe the various types, but 
rather to explain those underlying principles which are common to 
all. A motorman cannot be too strongly advised to study the par- 
ticular types in detail which he is called upon to use, so as to know 
exactly the whereabouts of such things as motor cut-outs, etc., also 
as to what fingers are the best to be detached to replace a broken 
trolley finger, for instance, and in general to make himself perfectly 
familiar with the construction and working of the types he has to 
handle. 

The controller has not only to act as a starting switch, by means 
of which the necessary resistance may be inserted until the motor 
speeds up, and so develops the requisite back E.M.F., but it has also 
to perform the necessary operations, when so required, of placing the 
motors either in series or in parallel, reversing the motors, and also 
to place them in parallel as dynamos, where the controller is designed 
for electric braking. Taken in order, these various steps are as 
follows : — 

(1) To connect the motors in series with a certain amount of 
regulating resistance in circuit. See Fig. 31, a, 

(2) To gradually cut out the resistance, placing the motors finally 
in full series. See Fig. 31, h. 

(3) To connect the motors in parallel with a certain amount of 
regulating resistance in series with them. See Fig. 31, c, 

(4) To gradually cut out this resistance, placing the motors finally 
in full parallel. See Fig. 31, d. 

The controller also enables the direction of rotation, and hence 



APPLICATION OF MOTORS TO TRACTION 155 

the direction of the car, to be reversed, either by reversing' the 
armature current or by reversing the fields, and enables the above 



O^OUEY WHEEL 

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Fig. 31. 



156 ELEMENTS OF ELECTRIC TRACTION 

four operations to be performed in the order given for the new 
direction of rotation. See Fig. 31, e. 

The particular connections shown correspond with those shown 
in Fig. 31, a, namely, the first notch in series, but, for a reversed 
direction of rotation, to that shown in Fig. '^l,a. Reversal in this 
case is brought about by reversing the direction of the current passing 
through the armatures, the fields being kept the same. 

Also, where designed for electric braking, to couple the motors in 
parallel as dynamos, see Fig. 31,/, and to regulate them as such by 
means of the rheostats, whether the car be travelling backward or 
forward.* This will be dealt with in detail in the next chapter. 

Reversal. — With reference to the reversing operations, it may be 
said in order to reverse a motor, a simple application of the left- 
hand rule will show that in order to reverse the direction of rotation, 
either the field, that is, the direction of the current through the field, or 
the direction of the current through the armature must be reversed. 

In some form of controllers, such as the B.T.H. B13, B18, and 
KIO, or Westinghouse 90M and 210 types, the fields are always 
kept the same, and the current through the armature is reversed. In 
others, such as the Dick-Kerr D.B.L form, C type, reversal of one of 
the motors is brought about by reversing the current through the 
field winding, the direction of the armature current being kept the 
same ; the other motor being reversed by reversing the current through 
the armature, the current through the field of this motor not being 
altered as regards its direction. 

In the ordinary type of controller, there are generally two drums, 
or barrels as they are termed, one the main barrel, and the other the 
reverse barrel. Fixed on these barrels are various contacts suitably 
connected to or insulated from one another, as the case may require. 

The various connecting cables from the motors and rheostats are 
led to a terminal board fixed in the controller case, and connecting 
cables are led from the terminal board to various " contact fingers," 
as they are termed, which fingers press on the desired contacts fixed 
on the above barrels when these are suitably operated. Thus, when 
the barrels are rotated, the various contacts are also rotated, and in 
this way are brought into contact with the correct contact fingers, 
and by this means the various and necessary connections are suitably 
made and broken as required. 

To prevent excessive arcing, a magnetic blow-out is very often 
fitted to blow out any arc that may be formed when breaking the 
circuits. 

Reverse Barrel. — This is a small barrel, by the operating of 
which the motors can be reversed, as regards their direction of 
rotation. Tliis barrel is generally so interlocked with the main 

* The couacctioQS showu correspond for direction of motion with Fig. ol, e. 



APPLICATION OF MOTORS TO TRACTION 157 

barrel that the main barrel cannot be operated until the reverse 
barrel is moved into one of its running positions, that is, its ahead 
or astern position. Also, in a similar way, the reverse barrel cannot 
be operated when once it has been moved until the main barrel has 
been put to its " off" position. The reason for this interlocking has 
already been dealt with. 

Main Barrel. — This is a larger barrel than the reverse one, and 
by the operation of this, the various connections are made for in- 
serting resistance in the motor circuit, putting the motor into series 
or into parallel, etc., as required. 

The handle for operating the main barrel is generally termed 
the power handle, in contradistinction to the handle employed for 
operating the reverse barrel, which is generally termed the reverse 
handle. 

These handles are removable, the reverse one only so when in its 
off position. 

Motor Cut-outs. — In addition to the above, in most controllers 
for traction work will be found, in some shape or other, two switches 
which enable either one or the other of the motors to be cut out. 
Thus, in the event of one motor breaking down, that motor can be 
cut out, and the car handled simply by means of the other. 

These motor cut-outs, in some forms of controllers — some of the 
B.T.H. types, for instance — are so interlocked with the controller 
barrel that in the event of one motor being cut out, the power handle 
cannot be moved past the full-series notch. 

In other words, when one motor is cut out, the other motor is 
simply operated on the series notches. 

In other types, such as the Brush Company's controllers, and 
some of the Dick-Kerr controllers, the remaining motor is worked 
only on the parallel notches. 

In the B.T.H. B13, B18, and KIO types the motor cut-outs 
consist of small separate switches. In the Westinghouse, No. 90M 
and No. 210 types, the motors are cut out by operating one of the 
reverse drums, a small brass knob being fitted for suitably discon- 
necting such. In the Dick-Kerr D.B.I, form, C type, the motors are 
cut out by pulling back one of the fingers at the side of the reverse 
drum, these fingers, numbered 1 and 2, being provided with catches 
to hold them off when so required. 

Controller Operations. — In order to form some idea as to what 
happens when a car is set in motion, and the function fulfilled by 
the controller, a concrete case will be dealt with in the simplest way 
possible, by assuming certain values of the current, and considering 
what takes place under a given set of conditions. 

It should be noted that any sudden increase in the value of the 
current means a sudden increase in the value of the draw-bar pull. 



158 ELEMENTS OF ELECTRIC TRACTION 

and the effect of this tends to give the car a sudden jerk, depending, 
of course, upon the amount of the increase. Whether starting or 
stopping a car, all such sudden jerking should be avoided as much 
as possible, not only for the comfort of the passengers, but to avoid 
any sudden straining of the motors and gearing. 

On putting the power handle on the first notch, the motors being 
quite stationary, the current flowing through the motors will depend 
upon the resistance placed in series with them. The current will set 
up a certain draw-bar pull, which should start the car in motion 
unless the resistance of the circuit is much increased, as might be 
the case with very dirty rails, for instance. In cases where the 
resistance is such as to cause a heavy current to flow on starting, the 
sudden jerk can be lessened by the motorman " easing off" the hand 
brake at the same time he puts on to the first notch in series. 

Putting into Full Series. — To make the matter as simple as 
possible, it will be assumed that a 10-ton car is fitted with two motors 
similar to the one of which particulars have already been given, and 
that the resistance is such that when the power handle is on the first 
notch 60 amps, pass down the trolley, and consequently 60 amps, 
pass through each motor. 

Each motor will then exert a draw-bar pull (see Fig. 30) of some 
1400 lbs., making a total draw-bar pull of some 2800 lbs. 

Taking the resistance to traction as 25 lbs. per ton, 250 lbs. 
will be required to overcome frictional resistance, and assuming the 
car to be on a gradient of 1 in 22, a force of some 1018 lbs. will be 
required to balance the gravitational pull ; thus a total pull of 1018 
-I- 250, namely, 1268 lbs., will be required either just to move or to 
keep the car in uniform motion when once a speed has been obtained. 
Thus a nett force of 2800 — 1268, namely, 1532 lbs., will be available 
for acceleration, that is, 1532 lbs. per ton, and this will give, roughly, 
an acceleration of 1^ miles per hour per second. 

As the car gets up speed a back E.M.F. is developed which tends 
to reduce the current ; if, however, as the back E.M.F. is developed, 
resistance be cut out at a suitable rate, the current can be kept fairly 
constant. The increasing back E.M.F. tends to decrease, and the 
decreasing resistance tends to increase the current value, and in this 
way the two actions can be made to approximately balance one 
another. Consequently, as the car gets up speed, by passing the 
power handle from notch to notch, the motorman can, if resistance 
be suitable, keep the average value of the current, and consequently 
the draw-bar pull, fairly constant. 

On reaching the full-series notch all the regulating resistance 
will be cut out, and the full pressure of 500 volts will then be across 
the outer terminals of the two motors, and as they are in series this 
means that each motor will have 250 volts across its terminals. 



APPLICATION OF MOTORS TO TRACTION 159 

N'ow, on referring to the diagram given, it will be seen that when 
60 amps, are passing through the motors, with 500 volts pressure 
across the terminals of each, the car will have a speed of slightly 
over 8 miles per hour. With half this pressure across the terminals 
of each motor, the motors being in series, the car will have approxi- 
mately half this speed. Hence when in full series the car will have 
a speed of some 4 miles per hour, and as the current up to now has 
been kept constant, the total draw-bar pull of 2800 lbs. will also 
have been kept constant, and an accelerating force of 1532 lbs. will 
have been continuously at work. 

Putting into Full Parallel. — If now the controller handle be 
moved on to the first notch in parallel, and the resistance in the 
circuit is such that the current passing through each motor is the 
same as before, namely, 60 amps., that is, 120 amps, down the trolley, 
the draw-bar pull will remain constant, and the car will continue 
accelerating at the same rate as before, namely, at the rate of li^ 
miles per hour per second. 

If now the resistance be such that on gradually passing from 
notch to notch, as the back E.M.F. rises, the current can still be kept 
constant, then the accelerating force will also be kept constant, and 
in this way the car will speed up with the constant acceleration of 
IJ miles per hour per second, until finally the full parallel position 
is reached. 

When on full parallel, as all regulating resistance will then be 
cut out, each motor will have the full 500 volts across its terminals, 
and consequently the actual speed given in the diagram ; that is, the 
car will be running at a speed slightly over 8 miles per hour, and the 
motors will be exerting a total draw-bar pull of 2800 lbs. 

After this, the car with an accelerating force still at work will 
continue to increase its speed, and, since no resistance is now being 
cut out, the current and draw-bar pull will gradually decrease. 
However, as long as there is an accelerating force at work the car 
will continue to speed up, but at a gradually decreasing rate, owing 
to the decreasing value of the accelerating force. 

When a speed of 11 miles per hour is reached, it will be seen that 
each motor will exert a draw-bar pull of some 634 lbs., making a total 
of 1268 lbs. As this is just sufficient to balance the resistance to 
traction and gravitational pull due to the gradient of 1 in 22, the 
motors will cease to accelerate, and will continue to maintain 
the speed of 11 miles per hour, the current then passing through 
each motor being 35 amps., a total of 70 amps, passing down the 
trolley. 

The rheostats in actual practice are, in a great many cases, 
adjusted so that practically a uniform acceleration can be main- 
tained, as indicated above, until the full parallel position is reached. 



i6o ELEMENTS OF ELECTRIC TRACTION 

Running on Full Series. — If, instead of moving into parallel, 
the power handle had been kept on the full-series notch, a similar 
action would have taken place on the full series as that which took 
place on the full parallel. Previously, on just reaching the full series 
the car had, as shown, a speed of 4 miles per hour, and the motors 
were exerting a total draw-bar pull of 2800 lbs. If, however, one 
had continued to run on the full-series notch, the motors would have 
continued to accelerate at some decreasing rate just as before, due 
to the decreasing current consequent upon the increasing back E.M.F., 
until a speed of approximately 5^ — one-half of 11, due to the motors 
being in series — miles per hour had been reached, the total draw-bar 
pull then of 1268 lbs. being just sufficient to balance the frictional 
and gravitational forces. The motors would then have ceased to 
accelerate, and the uniform speed of 5^ miles per hour would have 
been maintained, the current then passing down the trolley and also 
through the motors being 35 amps. 

It will thus be seen that if the car is allowed to run either on 
the full-series or the full- parallel notch, some uniform speed is 
finally reached, and all accelerating effort ceases, unless new condi- 
tions arise in some way or other to alter matters. 

If, from any cause, the total pull required to maintain motion 
increases, such as would be brought about by an increase in weight 
or an increase of gradient, the car will slow down, the draw-bar 
pull and power increasing, until again some balance is reached, the 
car then maintaining some uniform but lesser speed. 

If, on the other hand, the total pull required decreases, the car 
will speed up, the draw-bar pull and power decreasing until again 
some balance is reached, the car then maintaining some uniform 
but higher speed. 

Late Paralleling. — If, after running on the full-series notch, 
the power handle be moved over so as to pass into parallel, it is 
interesting to note the kind of action that will then take place. 

Previously, when full series has been reached just previous to 
passing into parallel, 60 amps, were passing through the motors, 
and the car was travelling, for the time being, at a speed of some 
4 miles per hour, 250 volts being across the terminals of each 
motor. 

In the case that is now being considered, after running on full 
series 35 amps, are passing through the motors, and the car is 
running at a uniform speed of some 5^ miles per hour, 250 volts, 
as before, being across the terminals of each motor. In consequence 
of this higher speed, a greater back E.M.F. is being generated, as 
indicated by the decreased current of 35 amps., as against the 60 
amps, in the previous case. On account of this higher back E.M.F., 
when the motors are put into parallel, a less current than 60 amps.. 



APPLICATION OF MOTORS TO TRACTION i6i 

will flow through each motor, but, on the other hand, there will be a 
greater current than 35 amps., the reason of this being as follows : — 

In the first case that was considered, as the current did not alter 
its value when the motors were put into parallel — the back E.M.F., 
roughly speaking, on full series being very little different from that 
when on first notch in parallel — the drop in pressure in the resistance 
had to be such as to keep the pressure across the terminals of the 
motors approximately the same as when they were in series, namely, 
250 volts, a drop of 250 volts therefore taking place in the resistance. 
This took place when 120 amps, were passing through the regulating 
resistance in circuit. If, now, in the case under consideration, some 
less current than 60 amps, passes through each motor, a less current 
than 120 amps, will pass through the resistance, and, in consequence, 
a less drop than 250 volts will take place, and therefore a higher 
pressure than 250 volts will be across the motor terminals, and hence 
a greater current than 35 amps, through each motor. In short, as 
stated above, a current will flow having a value somewhere between 
35 and 60 amps. 

Assuming a likely value, say, of 45 amps., it will be seen that 
after running on series and passing into parallel, the draw-bar pull 
will be increased from a total of 1268 lbs. to a total of 1880 lbs., an 
increase of 612 lbs. thus taking place with the increase of 10 amps, 
through each motor; this means there will now be at work an 
accelerating force of 612 lbs. A jerk might be noticed, due to this 
sudden increase, but as this increase is only small compared with 
the 1532 lbs. accelerating effort, when the car is started the jerk will 
be correspondingly less. 

The accelerating effort of 612 lbs. will give an acceleration of 
some j% mile per hour per second, and if resistance can be cut out 
at some correspondingly slow rate, so as to keep the current of 45 
amps, fairly constant, an acceleration of ^^ miles per hour per second 
will take place, until finally, when all resistance is cut out, the car 
will have obtained a speed of some 9 J miles per hour. The car will 
then continue to speed up at some decreasing rate, until a speed of 
11 miles per hour is reached as before. With the slower rate of 
acceleration a longer time will be taken in obtaining a given increase 
in speed. 

In actual practice, what will in all probability take place, is, that 
the motorman will cut out resistance at a greater rate, thus increasing 
the 42 amps., say, up to 60, and in this way obtaining finally the 
previous rate of acceleration of IJ miles per hour per second, pro- 
vided no alteration has taken place in the gradient. 

In this case the draw-bar pull will gradually increase, if resistance 
be cut out, fairly uniformly from 612 lbs. to 1532 lbs. ; the average 
rate of acceleration in passing from first notch in parallel to full 

M 



i62 ELEMENTS OF ELECTRIC TRACTION 

parallel will be higher than in the case just considered, and the car 
will speed up in quicker time. The rate of acceleration will not, 
however, be as uniform, and the average accelerating force will not 
be as great as in the original instance, where 1532 lbs. accelerating 
effort was continuously at work, and consequently the time taken 
will be longer for any given increase in speed. 

The practical outcome shows that staying too long on series, 
paralleling too late, as it is termed — that is, when it is not desirable 
to run on the series notch — only causes a reduction of the current, 
a liability to some slight jerking action when moving into parallel, 
due to the varying value of the accelerating force, and a longer time 
taken to accelerate to a given speed. 

On the other hand, moving into parallel too early at starting only 
wastes energy. As already indicated, the current passing down the 
trolley can be increased to double its value with the motors in 
parallel without any increase being made in the draw-bar pull. 

From above it will be seen that anything that causes the current 
to be suddenly increased, such as unsuitable resistance, too few 
notches, or cutting out resistance too quickly, that is, at a greater 
rate than the back E.M.F. is increasing, will cause the draw-bar 
pull to be suddenly increased, and a jerking effect and variable 
accelerating effort will be the outcome. • 

Regenerative Systems. — Regeneration. — Regeneration, as ap- 
plied to electric traction, means the regenerating of electrical energy, 
or the converting again of the energy that has been imparted to a 
car into electrical energy, with the idea of utilizing the energy so 
recovered for useful purposes. 

In imparting motion to a car, a certain amount of the energy 
expended becomes converted into heat, due to friction of one kind 
and another. As the heat will have been dissipated in various ways, 
the recovery of the energy expended in this direction is quite out of 
the question. 

On the other hand, a certain amount of energy has had to be 
expended in giving to the car its kinetic energy ; that is, the energy 
the car possesses by virtue of its motion. Also a certain amount of 
energy has had to be expended in giving to the car its potential 
energy ; that is, the energy the car possesses simply by virtue of its 
position, where the car has mounted a gradient. 

Now, the energy expended in giving to a car both its kinetic and 
also its potential energy becomes stored up in the car, as it were, 
and can therefore be recovered to a certain extent, less, of course, 
the losses which are bound to take place in the recovering process. 

Before a car can be brought to rest — as energy cannot be 
destroyed — it will have to be robbed of its energy of motion, and 
when so robbed, it will come to a standstill. This energy of motion 



APPLICATION OF MOTORS TO TRACTION 163 

will depend not only upon the speed the motors may have given 
to the car, but also upon any additional speed the car may have 
obtained in descending a gradient, the energy due to this additional 
speed being derived from the potential energy ; that is, the energy 
previously spent in moving the car up the incline. 

Therefore, before a car can be brought to rest, the kinetic energy 
that it possesses at any particular moment, whether on a gradient or 
on the level, will either have to be converted into some other form of 
energy or it will have to be transferred to some other body. 

In the ordinary way, to bring a car to rest, or to control its speed, 
friction brakes, or electric brakes of some kind or another, are 
generally employed. When friction brakes are adopted, the energy 
stored up in the car is converted directly into heat, and in this way 
is wasted. When ordinary rheostatie electric braking is employed, 
the energy stored up in the car is converted into electrical energy, 
but the electrical energy so generated is simply wasted in heating 
up the resistance placed in the circuit. 

In regenerative systems the object is to convert the energy that 
can be recovered into electrical energy, and to utilize the electrical 
energy so generated. For this purpose the pressure generated is 
employed to send current back to the trolley wire, and in this 
way assists the main generating plant in supplying electrical 
energy to the system. This means, also, that an electric braking 
action is obtained when regeneration takes place, the motors having 
to be driven as dynamos. 

The power regenerated in this way, it is claimed, not only relieves 
the generating station, but also enables size of cables, feeders, etc., 
to be reduced. The saving in electrical energy claimed varies from 
15 per cent, to 30 per cent., and more, depending upon the nature of 
the line, etc. 

In Birmingham, where some tests have been made with Mr. 
Kaworth's regenerative system, the consumption averaged 0*97 
Board of Trade unit per car mile, the usual figure under similar 
conditions with the ordinary series system being 1'2 units per car 
mile, this representing a saving of some 19 per cent. 

A further saving is also claimed in repairs, wear and tear of 
wheels, brake-blocks, etc. Here again in Birmingham the saving in 
repairs on the cars^ amounted to no less than six-sevenths of the 
ordinary cost, as ascertained by comparative tests. 

The saving in braking is due to the fact that the driver has much 
greater control over the speed of the car, and instead of slowing a 
car down by means of the hand brake, can either run very slowly 
along, or even be regenerating when moving through congested 
traffic. Naturally, the best results with these regenerative systems 
are obtained in hilly districts. 



i64 ELEMENTS OF ELECTRIC TRACTION 

From what has already been seen of the characteristic behaviour 
of dynamos, it will be understood that in order to send current back 
to the trolley, some form of dynamo must be employed which will 
give a fairly constant pressure, whether on light or heavy loads, that 
is, whether sending back a small or a large current. Thus a shunt 
or compound dynamo would be suitable for such a purpose. 

In one of these regenerative systems a shunt motor is employed, 
which also acts as a shunt dynamo when regenerating. In the other, 
by a special field- changing device, the motors, which are arranged 
to act as series motors when driving the car, are converted into 
a type of compound dynamo when employed for regenerating 
purposes. 

Whatever type of dynamo is employed, the pressure generated 
must exceed that of the trolley wire if current is to be sent back, 
the trolley pressure acting as a back E.M.F. to the motors then acting 
as dynamos. In this way, regenerative systems have the benefit that 
the motors, when acting as dynamos, cannot readily be overloaded, as 
is often the case when they are employed for ordinary electric braking. 

Braking. — Another advantage claimed for regeneration is in 
connection with braking. 

In many cases where ordinary electric brakes are fitted to a car, 
they are not employed for general braking purposes, but only in 
cases of emergency. The reason for this is, that serious overloading 
of the motors when acting as dynamos is apt to take place when 
such braking is employed. The result of tliis is, the motorman does 
not become perfectly familiar with, and dependent upon, the use of 
such brakes. Also, there is the danger of these brakes being out of 
order with such occasional use unless daily examination is made. 

In the regenerative systems, every time a man retards the car's 
motion, regeneration to a greater or less extent takes place ; in other 
words, an electric braking action goes on. The motorman in this 
way learns to rely upon this means of retarding the motion of a car, 
and any failure in the retarding or braking action is at once noted. 

The wheels cannot, of course, be brought to a standstill by re- 
generative braking, because, when the speed becomes reduced to a 
certain value, the pressure generated falls below that of the trolley, 
and the trolley pressure then being the greater, current is supplied 
to the motors. In short, the wheels will always revolve as long as 
the circuit is complete, unless they are jammed by means of the 
hand brake, and to stop the car mechanical or rheostatic braking of 
one kind or another has in consequence to be adopted. Consequently 
a more perfect and complete control of the car under all ordinary 
conditions is obtained in the regenerative systems, as a car when 
not receiving electrical energy is either restoring energy or is actually 
being brought to a standstill. 



APPLICATION OF MOTORS TO TRACTION 165 

As already stated, two regenerative systems at the present time 
are being put forward in this country. One by the Raworth's Traction 
Patents, Ltd., and the other by the Johnson-Lundell Traction Co., 
Ltd. A brief description of these two systems will now be given. 

Raworth's Regenerative System. — In this system a special 
design of shunt motor is employed, which, when regenerating, acts 
as a shunt dynamo. 

Speed variation is chiefly obtained by varying the field strength, 
this being brought about by means of a suitable shunt regulator, 
which enables resistance to be either inserted or cut out of the shunt 
circuit as desired. In this way the exciting current is varied, and, 
in consequence, also the field strength. 

A certain loss of energy, in addition to that taking place in the 
field, will, of course, take place in the regulating resistance, the pro- 
portion of energy expended in each being proportionate to their 
respective resistances. 

This method of varying the speed, it will be seen, is of a very 
simple character, and variation can in this way be obtained from 4 
to 14 miles per hour, or from 6 to 21 miles per hour. 

On starting a car the field circuit is completed first, that is, 
before the armature circuit, and as all regulating resistance is cut 
out of the shunt circuit at this stage, the field has its maximum 
strength, and the car is given its minimum speed. 

To increase the speed of the car the field is weakened, resistance 
for this purpose being inserted in the shunt circuit by means of the 
shunt regulator. It should be noted here that with every variation 
in the strength of field there will be a variation in the speed. 

To retard the motion of the car at any time — unless the speed is 
such a very low one that regeneration cannot be carried out, in which 
case mechanical or rheostatic braking is employed — the field is simply 
strengthened. With the increased field strength, the back E.M.F. 
now generated by the motor will exceed that of the supply — that 
is, until the car's speed becomes reduced to its corresponding value 
— and current will be sent back to the trolley, regeneration thus 
taking place. The motors during this stage act as dynamos, and, 
in consequence, a retarding or braking action takes place when so 
regenerating. 

The stronger the field is made, or the greater the speed, the greater 
will be this retarding or braking action, also the greater will be the 
E.M.F. generated, and, in consequence, the greater will be the value 
of the current sent back. 

Regeneration in this system is also automatic in the following 
sense : With a given strength of field there will be practically a 
given speed, whether the car is mounting or descending a gradient. 
In mounting the gradient, the motors will be receiving energy from 



i66 ELEMENTS OF ELECTRIC TRACTION 

the trolley, the energy being expended in propelling the car up the 
gradient, whereas in descending the gradient the motors will be 
delivering electrical energy — in other words, regenerating. This 
will take place without the controller handles being operated, 
and, consequently, in this sense, the regeneration is automatic in 
character. 

The reason for the above is as follows : — 

As already seen, a shunt motor is practically a constant-speed 
motor under all loads, that is, with a given strength of field and a 
given voltage of supply. Under these conditions, very little variation 
in the speed with varying load is requisite to bring about the corre- 
sponding small change in the back E.M.F. for the required change 
in the value of the armature current. On very light loads the back 
E.M.F. generated will be almost equal to the voltage of supply, 
and if the load be entirely taken off, and the motor be driven — ^this 
corresponding to the case of a car descending a gradient — a slight 
increase in the speed will cause the E.M.F. generated to exceed that 
of the supply, and current in this way will be delivered to the trolley. 

In short, with a shunt motor with a given strength of field and 
a given terminal voltage, whether taking or delivering energy, the 
variation in the speed will not be great, and consequently, when 
applied to traction, the car's speed under these conditions will be 
practically uniform. 

Some of the advantages claimed for the shunt motor as applied 
in the above system, and as compared with the ordinary series motor 
in the series parallel system, are as follows : — 

Independence of Speed with regard to Load. — The speed 
of a shunt motor, the field being practically constant, varies very 
little, as already seen, with variation in the load — that is, whether 
developing a large or small horse-power. 

Applied to traction work, this means that a shunt motor, whether 
mounting a gradient or running on the level, will practically main- 
tain the same speed without any regulation, due to the fact that 
very little variation takes place in the speed with varying values 
of draw-bar pull and horse-power. Consequently, with a shunt 
motor with a given field strength, one uniform speed will practi- 
cally be obtained on all conditions of gradient, and variations in 
the field strength — which, as seen, can very readily be obtained 
in the above system — will bring about corresponding changes in the 
speed of the car. 

A Lesser Decrease in Draw-bar Pull with Increase ot 
Speed. — In the above system, a saturated field is employed, and as 
the maximum field strength is practically obtained when saturation is 
reached, the maximum draw-bar pull that a motor of given dimensions 
can exert, will, under these conditions, also be obtained — that is, as 



APPLICATION OF MOTORS TO TRACTION 167 

far as the field strength is concerned. In short, whatever be the 
means of excitation, the iron cannot be worked to more than its full 
limit, and consequently, by employing a saturated field, Mr. Raworth 
obtains the same maximum draw-bar pull with shunt excitation as 
can be obtained with series excitation. In fact, in some cases series 
motors have been taken and rewound as shunt motors. 

If reference be made to the actual figures of the series motor 
previously given, it will be seen that at the lower speeds, that is, 
when the motor is exerting its maximum draw-bar pull, there is a 
rapid drop in draw-bar pull with increase of speed. 

This result is due to the fact that in ordinary series motors, 
field strength and armature current are dependent upon one another. 
Thus, in a series motor a weakened field means also a weakened 
armature current. With shunt motors regulated in the manner indi- 
cated above, a weakened field does not necessarily mean a weakened 
armature current, field and armature currents in this case being 
independent. 

The result of this is, at the higher speeds a greater draw-bar pull 
can be obtained with a shunt motor than with the equivalent 
ordinary series motor at the same speed. Thus, a higher speed can 
be maintained on a given gradient without increasing the maximum 
speed of the motor, and in this way a greater range of speed regulation 
is obtained. 

With the higher speed on a given gradient, a greater armature 
current will be taken and a greater amount of power developed — in 
fact, with shunt motors so regulated, more power can be obtained at 
the higher speeds than with the ordinary and equivalent series motor. 
In this way a better average accelerating effort is obtained over a 
wide range of speed. A motorman has, in consequence, either with 
this system or the Johnson-Lundell System, much greater control 
over the speed of a car, and has not simply to take one of two speeds 
which the motors may give. 

It must be pointed out here that in the Johnson-Lundell System, 
similar speed variation is obtained with series motors. In this 
system, however, the field is also made, to a certain extent, inde- 
pendent of the armature current, and, consequently, similar results 
can be obtained, as in the above. The arrangement, however, as 
will be seen, is not so simple, and to convert the series motors into 
compound dynamos for regenerating purposes an additional and 
automatic controller has to be added to the equipment. 

Controller. — With regard to the controller, originally Mr. 
Raworth employed a different type from that in general use in the 
series-parallel system. The controller handles had a fore and aft 
motion, one being on each side of the controller. They were inter- 
locked in a similar way to the ordinary controller, and to suit the 



1 68 ELEMENTS OF ELECTRIC TRACTION 

special requirements of the shunt motors, such as exciting the field 
before closing the armature circuit, etc. Mr. Eaworth has, however, 
now adopted, in addition to the above means of regulating the speed, 
that also of series-parallel control for use with the shunt motors. A 
new form of controller has also been designed similar to the general 
type in outward appearance, the handles now being at the top and 
rotated in the usual way, each position of the regulating handle also 
corresponding to a certain speed of the car. Speeds in this way on 
the series notches can be obtained from 5 to 10 miles per hour, and 
on the parallel notches anything up to 20 miles per hour. 

When the speed is insufficient to generate a sufficiently high 
E.M.F. to send current back to the trolley, a braking action can be 
obtained by shortcircuiting the motors through a resistance ; in this 
case a rheostatic braking action is obtained independent of the line 
current. 

In the event of the trolley pole leaving the wire all regenerative 
braking ceases. In the later equipments a switch is added, which in 
such cases — when the E.M.F. generated by the motors exceeds a given 
amount — automatically closes the circuit through a resistance, thus 
bringing about automatically a rheostatic braking action. This also 
meets a difficulty which has arisen in these instances due to the 
E.M.F. generated bursting the car lamps, etc. 

The Johnson-Lundell Regenerative System. — In this system, 
as already indicated, series motors are employed. Speed variation is 
obtained partly by series-paralleling the motor circuits, and partly 
by varying the field strength. The circuits are paralleled twice, 
thus necessitating the employment of four instead of two armature 
circuits. These may consist of either four separate motors, or simply 
two motors, each motor having two separate windings on the same 
armature core, and two commutators on the same armature shaft to 
correspond. In the latter case one field is common to the two 
armatures. 

By means of this double series paralleling in combination with 
strong magnetic fields, which are also to a certain extent variable, 
main circuit resistances in this system are dispensed with, and nine 
out of the ten notches on the controller are running notches, the first 
being merely a starting notch. 

On some tests made at the above company's works, speeds 
ranging up to 17 miles per hour were obtained, and regeneration 
commenced at once when desired, and was continued down to speeds 
not more than 2 miles per hour. 

The motors, when acting as such, namely, when driving the car, 
are series excited ; the main current, however, in this system does 
not simply pass through one set of field coils, as is the case in an 
ordinary series motor, but passes through a number of coils, some of 



APPLICATION OF MOTORS TO TRACTION 169 

which are fixed-series turns, and some of which are in parallel with 
one another, the whole, however (treating it as such), forming a 
series winding. 

The coils, which are in parallel with one another, it may be said, 
are fine-wire coils, and when regenerating, these coils are placed 
in series with one another, and so form the shunt portion of the 
compound winding. When placed as indicated above, in parallel, 
they form a portion of the series winding for the motors. 

Variation of the field strength is obtained by diverting a portion 
of the main current through diverting resistances. 

On the first three running notches, all four armatures are in 
series with one another, together with the two fields. Variations 
in speed are obtained by varying the field strength, this being 
obtained by diverting a portion of the main current through diverting 
resistances, as mentioned above, so that the whole of the armature 
current in these cases does not pass through the series windings. 
In this way the field becomes slightly weakened, and the speed 
correspondingly increased. 

On the next three notches, two of the armatures are placed in 
series with one another and their corresponding field, the whole 
being in parallel with the other two armatures and their field. 
Further variations in speed are obtained by again diverting a portion 
of the field current. 

On the next and last three notches, two of the armatures are 
placed in parallel with one another and in series with their field 
winding, the whole being in parallel with the other two armatures and 
their field, further variations in speed being obtained as previously. 

When regenerating, that is, when braking, those field coils which 
were placed in parallel previously, and formed part of the series 
winding, are now placed in series, and form the shunt portion of the 
compound winding. 

The series portion of the compound winding acts in opposition 
to the shunt winding, and thus its tendency is not to keep the 
voltage constant, as is attempted in an ordinary compound dynamo, 
but to reduce the voltage slightly on heavy loads. For this purpose 
the series windings are only few in number, and, in addition, are 
shunted to a certain extent. In practice this arrangement has been 
found to be of advantage in preventing sudden heavy rushes of 
current when regenerating. 

The motors, when acting as dynamos, go through a similar but 
reverse cycle of changes, from full parallel to finally full series, thus 
a variable braking effect is obtained such that regeneration, it is 
claimed, can take place when the car is moving no faster than a slow 
walk. Thus, every time a car is stopped, checked, or restrained on 
an incline, a certain amount of electrical energy is recovered. 



170 ELEMENTS OF ELECTRIC TRACTION 

The above various field changes are obtained by the employment 
of a special device, which is called the "field changer," this being 
operated automatically, the motorman bringing it into operation by 
thumb pressure on a lever fixed on the controller handle. 

In operating the controller, the various changes of the circuits, 
etc., which are effected by the forward movement of the controller 
handle for the purpose of acceleration, are made in the reverse order 
when the handle is moved backward, but are without effect for 
regenerating, if the lever on the controller handle is not operated. If, 
however, this be operated, the field-changing device automatically 
brings about the requisite changes — the field winding now being a 
compound one — and so enables the motors to develop a retarding 
or braking effect as the handle is moved backwards in the same 
graduated way as they developed an accelerating effect when the 
handle was moved forward. 

In this system, regeneration is not automatic in the same way as 
in the previous system, the motorman having to operate by thumb 
pressure a small operating lever, which allows the requisite field 
changes to be automatically made, and which converts the series 
motors into compound dynamos for regeneration. 

In this system, when the speed falls to one mile per hour or so, 
regeneration is not attempted, but an automatic mechanical braking 
device is substituted for finally stopping the car and holding it. 

In the event of the electrical circuit being broken in any way 
whatever, the above mechanical brake is automatically brought into 
operation without the intervention of the driver. 



CHAPTER X 
BRAKES 

Brakes as applied to ordinary tramway traction have, roughly 
speaking, two functions to fulfil — 

1. To enable the car to be brought to rest, or its speed to be 
reduced. 

2. To enable the car to be held at rest, on any gradient it may 
be on. 

To satisfactorily perform these apparently simple requirements 
under all the varied conditions and circumstances which arise in 
practice, is, however, by no means an easy or a simple matter, and 
various types of brakes — some mechanical and some electrical — 
have been adopted. 

In this chapter no attempt will be made to describe the con- 
structional details of any particular type of brake, but rather to 
explain the principles which underlie all braking actions, and the 
actions which take place when the various types of brakes are 
employed for the purpose of retarding the motion of a car, and more 
particularly the actions which take place when the electric motors are 
employed in some form or another for retarding or braking purposes. 

General Principle. — The principle of the conservation of energy, 
viz., that energy cannot be destroyed, has a very definite and direct 
application in the stopping of a car in motion. 

The energy expended in imparting motion to a car, as previously 
pointed out, becomes converted chiefly into three forms of energy — 

1. Heat energy — due to friction. 

2. Potential energy — the energy a car possesses by virtue of its 
position. 

3. Kinetic energy — the energy a car possesses by virtue of its 
motion. 

As the energy expended in overcoming friction becomes converted 
into heat, and as the energy expended in raising a car up a gradient 
becomes stored up in the car simply by virtue of its position, the 
only energy that need be considered in the stopping of a car is simply 



172 ELEMENTS OF ELECTRIC TRACTION 

that which the car possesses at any moment by virtue of its motion, 
that is, its kinetic energy. 

The car's kinetic energy is therefore the energy which must be 
converted either into some other form of energy, or else be transferred 
to some other body — as it cannot be destroyed — before the car can 
be brought to rest. 

Where mechanical or electrical brakes, as at present adopted, are 
employed — with the exception of the systems where regeneration is 
carried out — the kinetic energy that the car possesses always becomes 
directly or indirectly converted by means of the brakes into heat, 
and in consequence is dissipated in various ways. The kinetic 
energy in such cases is not in consequence utilized — whether this 
energy is utilized or not is, however, simply a matter of economy — 
but the faster this kinetic energy is converted into some other form 
of energy, the quicker will the car, of course, be brought to rest. 
This converting of the kinetic energy, then, is the object of all brakes 
of whatever form or type. 

Having brought a car to rest, if it is on a gradient, a force of 
some kind will have to be employed — unless the gradient is a very 
slight one, when the tractive resistance of itself will be sufficient — 
to balance the gravitational pull, and so prevent it running down the 
incline. In other words, brakes will again be required, to hold the 
car at rest. In this case, if a force were not applied, the potential 
energy would become partially converted — as friction has to be over- 
come — into kinetic energy, or, in other words, the car would descend 
the gradient gaining speed, and so energy of motion. 

Thus, for example, a 10-ton car starting from rest, on descending 
a gradient of 1 in 10, would, it may be said, gain of itself, that is, 
without the motors being employed in any way — assuming a tractive 
resistance of 25 lbs. per ton — a speed of over 28 miles per hour in 
travelling a distance of 100 yards down such a gradient, and in 
travelling the 100 yards some 266 foot-tons of potential energy 
would be converted into kinetic energy ; in fact, as the motors would 
not have imparted any motion to the car, its entire kinetic energy at 
the instant under consideration would have been derived from the 
car's potential energy, in other words, from energy previously 
expended in raising the car up to its present level. 

If the car started at some uniform speed down the gradient, then, 
if it were not to increase its speed, the potential energy, less that 
required for overcoming frictional resistance, would have to be 
converted by means of the brakes into some other form of energy, 
otherwise some of this energy would be expended in accelerating 
the car. 

If a car were mounting a gradient, the gravitational pull would 
assist the braking action, as in this case some of the kinetic energy 



BRAKES 173 

would be expended in raising the car up the incline ; that is, would be 
converted into potential energy. 

Kinetic Energy. — The value of a car's kinetic energy depends 
not only upon the total weight of the car (passengers included), but 
also largely upon the speed ; in fact, it varies as the square of the 
speed. Thus in any given case, to double the speed of a car means 
that the kinetic energy would be increased to four times its original 
value ; three times the speed means that the energy would be increased 
to nine times its original value; and so on. 

The fact that the kinetic energy increases as the square of the 
speed, indicates the danger that arises when a car gets beyond control 
coming down an incline, as with a gain in speed there is a still 
greater gain in energy, and hence the increasing difficulty in success- 
fully braking the car, as the greater amount of energy has to be 
converted into some other form of energy before the car can be 
brought to rest. 

The actual value of the kinetic energy can easily be calculated if 
the weight and speed of the car be known. When dealing with 
draw-bar pull, it was seen how, in the case of a car starting from rest, 
the kinetic energy could be calculated if the accelerating force, and 
the distance the force was exerted through, were known. 

The following approximate rule, which is generally more applic- 
able, is a simple modification of that same method of calculating the 
kinetic energy : — 

Kinetic energy I _ (weight of car in tons) x (speed in miles per hour)^ 
in foot-tons j ~ 30 

This can be still further simplified when the car weighs 10 tons, 
the kinetic energy in foot-tons then being obtained by dividing the 
square of the speed in miles per hour by 3. 

Example. — The kinetic energy in foot-tons stored up in a 10-ton 

12 X 12 

car travelling at a speed of 12 miles per hour is equal to — ^j , 

namely, 48 foot tons, or 48 x 2240, namely, 107,520 foot-lbs. 

If the car were brought to rest in 10 seconds, or J minute, 
this energy would have been converted into some form or other, at 
the rate of 107,520 foot-lbs. per J minute ; that is, at the rate of 
six times 107,520, namely, 645,120 foot-lbs. per minute. 

If this energy were converted, say, into electrical energy, and 
utilized, assuming a total efficiency of say 70 per cent., useful work would 

have been done at the rate of ittttt , namely, 451,584 foot-lbs. 

100 j> ^ 

per minute, and this would be equivalent to -'sVo^oIt' iiamely, 13 '6 
E.H.P. 



174 ELEMENTS OF ELECTRIC TRACTION 

That is, energy stored up in the car in this case would be capable 
of supplying electrical energy at the average rate of 13"6 E.H.P., or 
lO'l kilowatts for the short period of time during which the car was 
being pulled up, namely, J minute ; in other words, electrical energy 
of the value of 0028 B.O.T. unit. 

As it is useful to be able to estimate the speed a car will attain 
on descending a gradient — the excessive speed attained in a given 
time in some cases hardly being realized — the first two of the follow- 
ing formulae have been specially drawn up to enable the speed a car 
wall attain to be approximately calculated, as indicated below : — 

(1) The first formula enables the approximate speed to be readily 
calculated that a car starting from rest will attain, in any given 
number of yards, on descending any given gradient, 

(2) The second enables the approximate speed to be readily 
calculated that a car starting from rest will attain, in any given 
number of seconds, on descending any given gradient. 

The speeds are those which would be attained simply due to 
gravitational effects, and not to any speed the motors might give to 
the car in addition, and on the assumption, of course, that no braking 
action is taking place, the only retarding force being that due to 
tractive resistance. 

The rule for obtaining the kinetic energy stored up in a car is 
also given in formula form, and various other formulse are added for 
enabling various calculations to be made, as briefly indicated below. 

Most of these formulae are simply modifications of well-known 
formulae used in mechanics, which have been modified specially for 
direct application to traction work : — 

W = w^eight of car in tons. 
S = speed in miles per hour. 
Y = distance in yards. 

A = acceleration in miles per hour per second. 
F = accelerating force in lbs. 
G = distance in feet a car travels up a gradient in order to rise 

1 foot. 
T = time in seconds. 

(1) S^ = Y — p based on an assumption of a tractive resist- 
ance of 25 lbs. per ton. 

Example. — What speed will a car attain starting from rest on 
travelling 100 yards down a gradient of 1 in 15 ? 

S2 = 100 ^^^^^ = 1^ X 5f = 500 
.-. S2 = 500 



BRAKES 175 

Therefore the speed attained will be approximately 22'3 miles 
per hour, 22'3 being the square root of 500. 

(2) S = ^^ "" based on an assumption of a tractive resistance 

of 25 lbs. per ton. 

Example. — What speed will a car starting from rest attain in 15 
seconds on descending a gradient of 1 in 15 ? 

(90- 15) 
60 



S = ^^^.-^^ X 15 = !-§ X 15 = 18| 



Therefore the speed attained in 15 seconds will be approximately 

18f miles per hour. 

WS^ WS2 

(3) Kinetic energy in foot-tons = -ok~' more accurately K(pJ^ 

(A) Kinetic energy in foot-lbs. = WS^ X 75, more accurately 
WS2 X 75-28. 

(5) F = A X W X 102, more accurately F = A x W x 102'66 

F X Y F X Y 

*(6) S2= ~^^ , more accurately S^ = ^^.^^ ^ 

(7a) S2 = 4AY, more accurately S^ = 4-09 AY 
(7b) A = -^y, more accurately A = ttaqy 

(8) S = AT 

AT^ AT^ 

(9) Y = -J—, more accurately Y = ^Taq 

(5) enables the accelerating force to be calculated, if weight of 
car and acceleration required be known. 

(6) enables the speed to be calculated that a car starting from 
rest will attain in a given number of yards, if the accelerating force 
and weight of car be known. 

(7a) enables the speed to be calculated that a car starting from 
rest will attain in a given number of yards, if the acceleration in 
miles per hour per second be known. 

(7b) enables the retardation in miles per hour per second to be 
calculated, if the speed a car is travelling at at any instant, and the 
number of yards it takes the car to pull up in, be known ; the letter 
A then representing the retardation in miles per hour per second. 

(8) enables the speed to be calculated that a car starting from 
rest will attain if the acceleration in miles per hour per second, and 
the time the acceleration is taking place, be known. 

* FormulflB 6 to 9 are based on the assumption that the acceleration or retardation, 
as the case may be, is of constant value. 



y 



176 ELEMENTS OF ELECTRIC TRACTION 

(9) enables the distance a car starting from rest will travel in a 
given time, if the acceleration and time be known. 

The actual means of dealing with the kinetic energy of a car will 
now be considered, that is, the various methods of braking. 

The brakes as used in tramway work can be roughly divided into 
two classes — 

1. Mechanical brakes. 

2. Electrical brakes. 

Mechanical Brakes. — These can be again divided into two 
classes — 

1. Wheel-brakes, or brakes which operate on the wheels or 
driving axles of the car. 

2. Track-brakes, or brakes which operate directly on the rails. 
The ordinary wheel-brake is generally operated by hand, while 

mechanical track-brakes are sometimes operated by hand and some- 
times by means of compressed air. 

Electrical Brakes. — These can be divided into three classes — 

1. Rheostatic brakes. 

2. Electro-magnetic brakes. 

3. Regenerative braking. 

In all the three types here considered the motors are employed as 
dynamos when braking. The rheostatic and electro-magnetic brakes 
are those generally fitted when series motors are employed, in the 
series parallel system, and this particular application of these types 
will simply be considered. 

Rheostatic Brakes. — In this type the series motors are em- 
ployed as series dynamos when braking, in this way bringing about 
a retarding action on the wheels, as will be seen in detail later. The 
current in this type of brake is not utilized, but simply heats up the 
regulating resistance inserted in the circuit. 

Electro-magnetic Brakes. — These brakes employ the series 
motors as series dynamos, and the current in addition is employed 
to operate electro-magnetically, either track, or wheel, or both types 
of brake. 

In both the above types the energy generated, however, is finally 
wasted. 

Regenerative Braking. — In regenerative systems, as already 
seen, the current is sent back to the trolley, and in this way the 
electrical energy generated is utilized. The retarding action in this 
case is due to the fact that the motors are employed as dynamos, 
energy having to be expended to rotate these as such, just as in 
ordinary rheostatic braking. 

In dealing with the various types of brakes, distinction must also 
be made between brakes which enable a graduated braking action to 
be obtained to suit the various needs and requirements, and those 



BRAKES 177 

which, strictly speaking, act only as emergency stops, and which do 
not permit of any graduation in the retarding or braking effect. 

Before dealing with the action of these various brakes, in order 
that the reader may understand the present position and practice 
concerning tramway brakes, the following extracts from the B.O.T. 
Rules (1906) with reference to brakes for electric tramways are here 
given — 

Board of Trade Regulations. — 

" 1. Every motor carriage used on the tramways shall comply 
with the following requirements, that is to say — 

"(b) The wheels shall be fitted with brake blocks, which can 
be applied by a screw, or by other means, and there shall be in 
addition an adequate electric brake." 

(Note. — Where, for a considerable distance, the gradients are 1 
in 15 or steeper, the following will be added to this regulation : 
" and a slipper-brake or other track-brake approved by the Board 
of Trade for use on the tramways.") 

(Note. — Where for a considerable distance the gradients are 1 
in 15 or steeper, the following regulation will be imposed : " VL 
The slipper-brake or other track-brake should be applied in descending 
all gradients of 1 in 15 or steeper.") 

From these regulations, it will be seen that the Board of Trade 
require each car to be fitted with a wheel-brake, and an adequate 
electric brake, and where the gradients are 1 in 15 or steeper, a 
slipper or other track-brake of approved design is also required. 
The majority of cars fitted with series motors for ordinary series 
parallel control, at the present time are in consequence fitted with 
either one or the other of the following combinations : — 

Hand-operated wheel-brake and a rheostatic brake — in some cases 
an electrical emergency brake taking the place of the 
rheostatic. 

Hand-operated wheel-brake and a slipper-brake operated electro- 
magnetically. 

Hand-operated wheel-brake" and a combined slipper and wheel- 
brake operated electro-magnetically. 

While other combinations are to be found, for instance, a 
mechanical track-brak^, operated either by hand or by power, in 
some cases taking the place of the electro-magnetic slipper-brake, 
the above are fairly representative combinations. 

The action of the different types already mentioned will now be 
briefly considered. 

Mechanical Brakes. — 

Wheel-brakes. — These generally consist of cast-iron brake-shoes, 
which, whan the brakes are operated, are forced by suitable brake 
gear agaiijigt th^ rims of the car- wheels. 



178 ELEMENTS OF ELECTRIC TRACTION 

Whether operated by hand or by power, their action is the same, 
namely, that of retarding by frictional means the rotation of the 
wheels, and hence the motion of the car. It will thus be seen that 
their action depends upon the rotation of the wheels. The greater 
the pressure with which the brake-blocks are forced against the 
wheels, the greater will be the friction, and the greater in consequence 
the retarding or braking action, that is, as long as the wheels are 
kept revolving. 

The kinetic energy of the car in this type of brake is simply 
converted by the friction into heat. 

In the ordinary hand type, the brakes are generally operated by 
means of a handle fitted with a ratchet attachment, so that the 
operating handle need not be turned continually round, but simply 
worked backwards and forwards ; in this way the motorman is always 
able to obtain the full leverage of the operating handle. The brake 
spindle when the brakes are being operated coils up a chain, which 
in turn operates levers, which force the shoes carried by the brake 
beams up against the rims of the wheels. A pawl or catch attach- 
ment operated by foot enables the brakes to be kept on when required, 
and spiral springs are arranged to pull the brakes off when the catch 
is released. 

While the ordinary hand wheel-brake is easily operated and 
applied, the great disadvantage with all wheel-brakes, whether 
operated by hand or by power, is the liability when put on hard 
of locking the wheels, and so causing the wheels to skid, the friction 
between the wheels and the brake-blocks is then so great that the 
wheels slip or skid on the rails without revolving. Flat places, or 
" flats," as they are called, are in this way formed on the rims of 
the wheels, the greasier the rail the more likely is this skidding 
action to take place. In skidding the retarding force is simply that 
due to the friction, which, under the circumstances, exists between 
the wheels and the rails due to the weight of the car. This friction 
is generally so small, especially if the wheels are in at all a greasy 
condition, that practically no braking action, such as is required, 
takes place, the car under these circumstances simply sliding along 
the rails despite the fact that the brake is hard on. In all cases of 
skidding it will therefore be seen that the brakes are really not acting 
at all, and it cannot be too clearly pointed out that it is essential in 
all wheel- braking that the wheels should be kept just revolving if a 
braking action is to take place, and that when the wheels cease to 
revolve all braking action, so far as the brake-shoes are concerned, 
ceases, as all friction of motion between the wheels and the brake- 
shoes then ceases, the two simply being locked together. 

In operating wheel-brakes, therefore, if a skid occurs, the motor- 
man should release the hand-brake somewhat, drop sand in front of 



BRAKES 179 

the wheels if travelling forward, behind if travelling backward, say, 
down a gradient ; and after the wheels have regained their motion to 
again apply the brake gradually. 

In the ordinary type of hand-brake, the brakes can only be 
effectively operated from one platform at one time, and it is necessary 
therefore, to slacken the chain at one end if the brake is to be applied 
from the other platform. 

On all these points, however, as will be again referred to later, 
the motorman cannot, on the one hand, be too clearly instructed, and, 
on the other hand, cannot make himself too familiar with the con- 
struction and working of the particular type of brakes he is called 
upon to handle. 

Track-brakes. — In some towns the slipper, or other approved 
track-brake, takes the form of a mechanical slipper-brake, which is 
operated in some cases by hand, a hand-wheel then very often being 
employed in place of an ordinary handle for operating, and in other 
cases by means of compressed air (Hewitt and Ehodes air track- 
brake). 

The slipper is generally faced with wood, and when the brakes 
are operated, these slippers are forced by a suitable arrangement of 
levers, etc., on to the rails. The retarding force in this case, as in 
the previous one, is that due to friction, the distinguishing difference 
being that in the wheel-brake the motion of the wheels is retarded 
by frictional means, whereas in the slipper-brake the motion of the 
car itself is retarded. The action of the brake does not therefore 
depend upon the rotation of the wheels, but simply upon the motion 
of the car. 

The kinetic energy of the car in this case also is converted, by 
means of the friction between the slipper and the rails, into heat. 

The action of a mechanically operated slipper-brake tends to 
relieve the wheels of the weight of the car, but it should never be 
sufiBcient to actually lift the car off the rails on account of the 
possibility of derailment. 

The mechanical slipper-brake has this great advantage over the 
wheel-brake, that not only is skidding of the wheels avoided, but 
also its action is independent of the rotation of the wheels, and 
therefore of any such skidding. 

The mechanical slipper-brake has also the following advantages 
over electro-magnetic slipper-brakes : — 

First, that if the car is derailed, the slipper-brake can still be 
applied, whereas the slipper portion of an electro-magnetic brake is 
dependent on the car being on the rails ; this will, however, be again 
referred to later. 

The second advantage is .that there is not the same liability for 
a mechanical track-brake to get out of order, as is the case where 



i8o ELEMENTS OF ELECTRIC TRACTION 

brakes are operated in any way electrically, such as, for instance, 
may occur with a bad or broken connection. 

On the other hand, these risks with electrically operated brakes 
can be considerably reduced where regular examination is made, and 
when the brakes are allowed to be in constant use. 

Hand-operated track-brakes, however, throw a considerable strain 
upon the motorman, as considerable force is generally required to 
operate these, and also the length of time it takes a man to operate is 
of no small importance, especially when the speeds are at all high, 
such as are likely to occur with ordinary electric traction. 

On the other hand, when operated by compressed air, the increased 
weight and upkeep of the equipment is a matter that has to be 
considered. 

Electrical Brakes. — Before dealing with the different types of 
electrical brakes, the following general explanations, which apply to 
all forms of electrical brakes, that is, where the motors are made to 
act as generators, are given — 

It has already been seen that a motor, if suitably connected and 
driven, that is, provided with mechanical energy, will run as a 
dynamo, and partially convert the mechanical energy supplied into 
electrical energy, the remainder of the energy being converted in 
various ways into heat. This principle is now largely used for 
braking purposes, and, broadly speaking, all such braking is electrical 
braking, the car's kinetic energy in these cases being converted in 
this way into electrical energy. In this way the car is robbed, as it 
were, of its kinetic energy, and by being so robbed is brought to rest. 

Another way of considering the action of an electrical brake is 
as follows : — 

When the motors are coupled up to act as dynamos, and a suitable 
circuit arranged so that current can flow, a force will have to be 
applied to drive the motors, and hence the wheels round. Now, the 
fact that a force is required to drive the wheels round shows that 
the action of the dynamos (calling the motors now dynamos, since 
acting as such) tends to resist the motion of the wheels, thus tending 
to stop them, and so braking the car. 

Difficulty is sometimes experienced in grasping the above fact, 
namely, that a force has to be applied to drive a dynamo round, and 
that either the greater the current, or the greater the field strength, 
or the greater both these are, the greater will be the force required. 
This can possibly be best illustrated by treating the whole matter 
from a magnetic point of view, just as was done in the case of the 
motor. 

In Fig. 32, let A represent the armature of a dynamo revolving 
in the direction shown, with current flowing down the conductors on 
the left-hand side of the armature core, and up on the right. In 



BRAKES 



i8i 



consequence of the current so circulating round the armature core, 
the core becomes magnetized in such a. way that the bottom portion 
is always of north polarity and the top south. Now, to revolve the 
armature in the direction shown means that it will have to be driven 
in opposition to the forces of repulsion and attraction, due to the 
magnetic poles in the armature core and those of the main field. 
The result is that to drive the dynamo round, a force will have to be 




DYNAMO 



Fio. 32, 



applied to overcome the resisting forces. The greater the current the 
dynamo is delivering (assuming field to be either of constant or 
increasing strength), the greater will be the force required to drive 
the armature round, as, with an increased current, the more strongly 
will the armature be magnetized, and the stronger the poles, the 
greater the force that must be overcome. 

The retarding force, or, more accurately, the retarding torque, 
exerted by each motor when driven as a dynamo will therefore 
depend upon the strength of field, and upon the armature current, an 



1 82 ELEMENTS OF ELECTRIC TRACTION 

increase in either or both of the above quantities bringing about an 
increased retarding or braking effect. 

The actual current flowing through the armature in any given 
case will depend upon the field strength, speed, and resistance in the 
armature circuit, the field strength and speed determining the E.M.F. 
generated. Therefore, the stronger the field, or the higher the speed, 
or the less the resistance in the armature circuit, the other quanti- 
ties remaining the same, tlie greater will be the retarding or braking 
effect produced. 

Where ordinary series motors are employed for braking purposes, 
as the armature current determines the field strength, the retarding 
effect will simply depend upon the speed at which the wheels 
revolve, and the resistance in the armature circuit. The higher the 
speed with a given resistance, or the less the resistance in circuit 
with a given speed, the greater will be the retarding effect produced. 
In short, the greater the speed of the car the greater will be the 
braking action with a given resistance in cii'cuit ; that is, with the 
power handle on a given brake notch. 

From this it will be seen that in all electric braking, that is, 
where the motors are employed as dynamos, the braking action is 
automatic in the sense that the greater the speed, and therefore the 
greater the retardation required, the greater is the retarding effect 
produced, provided the wheels are kept from skidding. 

A most important feature to be noted in connection with all 
electric braking, that is, when the motors are employed as above, is, 
that if the wheels cease to revolve, the dynamo ceases to generate an 
electrical pressure, current will then cease also to flow, and the 
resisting force, in consequence, also ceases ; in short, the braking 
action ceases. If skidding, therefore, takes place, all electric braking 
action ceases entirely. 

An electric brake, therefore, automatically does what a man does 
when he takes off his hand-brake as the wheels start to skid, and 
applies it again when they start to revolve, the electric brake ceasing 
to act when the wheels skid, and immediately acting when they 
begin to revolve. 

Strictly speaking, it must not be said, however, that the electric 
brake prevents skidding. What the electric brake does is to auto- 
matically take off and put on a braking action just as the wheels 
skid or revolve, as the case may be. The sudden application of the 
electric brake, however, may cause the wheels to be puUed up so 
suddenly that a skidding action may be started (especially if rails 
are at all " greasy ") unless sand be dropped, and the wheels thus 
started skidding may continue, despite the fact that when the 
wheels are skidding the brake is automatically " off," as the wheels 
are not revolving. If the wheels skid, just as with hand-braking, 



BRAKES 183 

the releasing of the brake and the application of sand enables them 
to regain their motion, and when the wheels once more revolve the 
brake can then be gradually applied again. The "greasier " the rail, 
the more tendency there is, of course, for the wheels not only to 
start but to continue skidding. 

It must be, therefore, remembered that all electrical brakes of 
the above description depend entirely for their action upon the 
rotation of the wheels, and therefore, when' applying such brakes, 
the wheels should be kept from skidding both by the use of sand 
if the rails are at all greasy, and the careful application of the 
brake. 

An electrical brake, it must also be noted, will not effectively hold 
a car on a gradient, that is, where brakes are at all necessary, a 
gradual slipping of the car, due to the gradient, with an electrical 
brake taking place, as no retarding force is exerted until an E.M.F. 
is generated and current flows through the circuit. In such cases a 
mechanical brake is therefore necessary for holding the car at rest on 
a gradient. 

One advantage of electric braking is that practically no physical 
effort is required on the part of the motorman in order to apply the 
brake, and the intensity of the braking action is independent of the 
man's physical strength. 

Another advantage is that wear and tear of wheels and brake- 
blocks is saved, but it must not be forgotten that the strain of electric 
braking is thrown on to the motors and gearing. 

In all the various types, the disconnection from the trolley wire, 
and the various connections which are required, are made, it may be 
said, by means of the controller when suitably operated. 

Rheostatic Brake. — In this form of electric brake, the pressure 
generated by the series motors, acting as series dynamos, is employed 
to send current through a variable resistance, the amount of resist- 
ance in circuit being varied by means of the controller, that is, when 
it is operated on the brake-notches. For this purpose the main 
barrel of the controller is so designed, additional contacts, etc., being 
added, that after the brake-handle has been brought to its " off " 
position, it can then be moved on to what are termed the " brake- 
notches." When on these notches, the, motors are coupled up so as 
to act as dynamos in parallel, a certain amount of regulating resist- 
ance also being inserted in the circuit. On moving the power handle 
from brake-notch to brake-notch, this resistance can be gradually cut 
out, till finally, when on the last brake-notch, all regulating resist- 
ance is cut out of the circuit, the dynamos then being simply short- 
circuited on themselves. By this means a large or small current 
can, with a given speed, be allowed to flow through the circuit, and 
a graduated braking action can in this way be obtained ; the greater 



1 84 



ELEMENTS OF ELECTRIC TRACTION 



the current the greater being the braking effect, the greatest braking 
effect being produced when all regulating resistance is cut out. 

When the wheels cease to revolve, the dynamo ceases to generate, 
and all braking action then ceases, regardless, of course, of whatever 
brake-notch the handle is on. As the current, and hence the brak- 
ing effect, is regulated by means of a regulating resistance, or 
" rheostat/' as it is sometimes termed, the term " rheostatic brake " 
has thus been adopted to describe this particular type of brake. 

As examples, the B18, B13, British Thomson-Houston, and the 



rm 

BLOWOin" 
COIL 



r' 



RHEOSTATS 



Al ^MATura^ i — •-i^ 



EJ 




Field 

VJiNDiNq 



y^JsMr^: 



/fA/LS 



V\\VV 



Fig. 33. 



D.B.I., form C, Dick-Kerr, are types of controllers designed for 
rheostatic braking. Fig. 33 shows in simple diagrammatic form the 
connections that are made in the B18 B.T.H. type of controller 
when the power handle is placed on the first of the brake-notches, 
the two motors then being coupled up to act as dynamos in parallel, 
as indicated. 

It may be said here, that in some cases the above arrangement is 
somewhat modified when the controllers are arranged, as they easily 
can be, for magnetic slipper-braking. 

By moving the power handle from brake-notch to brake-notch, an 
increased retarding or braking effect can with a given speed be 
obtained, as already mentioned. If, on the other hand, the power 
handle be moved rapidly over the brake-notches on to the last brake- 
notch, a very powerful and instantaneous braking effect will take 
place, the effect then being in the nature of an emergency stop. A 
large current under these circumstances will flow through the circuit, 
that is, if the speed is at all an appreciable one, and the wheels, of 



BRAKES 185 

course, kept from skidding. A very heavy strain in consequence is 
thrown in this case both on the motors and gearing, and the use of 
such stops is limited solely to emergency cases. As the sudden 
application of such braking action has a tendency to cause the wheels 
to skid, sand should always be dropped when such braking action is 
being applied. 

In rheostatic braking pure and simple, the electrical energy 
generated is wasted as far as all useful purposes are Concerned, the 
current simply heating up the resistances, armature, and field wind- 
ings, etc., in circuit, the kinetic energy of the car in this way being 
converted indirectly into heat. 

B.T.H. Magnetic Slipper or Track Brake. — In this type of 
brake, the series motors are employed as series dynamos, as in the 
ordinary rheostatic brake just considered, and the current is regulated 
in a similar manner by means of resistance, the controller also being 
practically identical with the one employed for rheostatic braking. 
The current, however, in this case also passes through magnetizing 
coils which are inserted in the circuit, and which operate the slipper, 
or brake-shoes, in the manner described below. 

On an ordinary single truck there are generally two shoes, one 
shoe being attached to each side frame. Each shoe is placed opposite 
and near to the rails, and is held clear of the rails when the brake is 
not being operated by means of springs. The coils for magnetizing 
the shoes are coupled in parallel, so that in the event of any injury 
to either one shoe or coil, the other shoe is still capable of operating. 
The coils are arranged so that when current passes through them, the 
steel shoes become strongly magnetized. When so magnetized, each 
shoe induces the opposite magnetic polarity in that part of tlie rail 
opposite the shoe, and the result of this is that when the brake is 
applied — the wheels revolving — the shoes are drawn hard on to the 
rails, the springs only being sufficient to hold the shoes oft' when 
the brake is not applied. Friction in this way is set up between the 
shoes and the rails, and an additional braking action thereby introduced. 

By this means, it will be seen, a slipper braking action is brought 
about by magnetizing the shoes electro-magnetically by means of the 
current generated. 

The braking action, it will therefore be seen, in this type of brake 
is twofold — 

1. The braking action due to the motors acting as dynamos, an 
action which tends to stop the wheels revolving, practically a rheo- 
static braking action. 

2. The slipper braking action, due to the friction between the 
magnetized shoes and the rails. 

The two actions, however, it should be noted, are entirely de- 
pendent upon the wheels revolving. 



1 86 ELEMENTS OF ELECTRIC TRACTION 

The kinetic energy of the car in this case, just as in the previous 
one, is ultimately converted in various ways into heat, partly, for 
instance, by heating up the resistances, armature windings, field 
windings, etc., in circuit. 

The action here, as with all electric brakes, is automatic in the 
following sense, namely, the greater the speed with a given resistance 
in circuit, the greater will be the current, and the greater, in con- 
sequence, the attraction between the shoes and the rails (that is, of 
course, within certain limits, depending upon the degree of satura- 
tion), and, consequently, the greater the braking effect not only due 
to the shoes, but also due to the retarding effect of the motors acting 
as dynamos. A graduated or emergency braking action can also be 
obtained with this type of brake just as in the case of the rheostatic 
brake. 

When the car is brought to a standstill, no current will flow, and 
the shoes will then no longer be magnetized, that is, to any extent, 
the only magnetism remaining being the residual magnetism, the 
springs already described then pulling the shoes clear of the rails. 

This type of brake, it may be said, can very readily be applied to 
any car fitted for rheostatic braking, and it also has the following 
advantages : — 

Less current, it is claimed, is needed for a given braking action 
than with the ordinary rheostatic type, consequently there is less 
heating of the motors, etc., and less wear of gear and pinions. 

With an ordinary mechanical track-brake the wheels are relieved 
somewhat of the weight of the car when the brake is applied, and 
unless suitably provided for, there is, of course, with these brakes, 
the consequent possibility of derailment. In the magnetic slipper 
type of track-brake, the reverse is the case, the adhesion between 
wheels and rails being increased when the brake is applied, there is, 
therefore, no risk whatever of the car being derailed due to this cause. 
There is also no additional increase in weight, or cost of extra equip- 
ment, as there is when slipper- or track-brakes are operated, by means 
say of compressed air. 

In some experiments that were made with the above type of 
brake, the following results, which were at the time published in 
the electrical press, were obtained with a four-wheel double-deck 
car fitted with two motors : — 

Travelling at 25 miles an hour down a gradient of 1 in 13 to 14, 
the car was pulled up in 25 yards, 4 seconds being the time taken. 

The same car travelling at 14 miles per hour on the level was 
pulled up in a little less than 5 J yards, the time taken being 1*6 
seconds. 

In each of the above cases the brake was simply used as an 
emergency stop. 



BRAKES 187 

The following tests were also made for graduated braking when 
coasting down a gradient : — 

A speed of 5 miles per hour was maintained on a gradient of 1 in 
13 to 14, the current per motor then being 4 amps. 

A speed of 5 miles per hour was maintained on a gradient of 1 in 
17, the current per motor then being 3*5 amps. 

A speed of 5 miles per hour was maintained on a gradient of 1 in 
45, the current per motor then being 2 amps. 

In the case of a car provided with this type of brake leaving the 
rails, provided the wheels are still revolving and the brake is applied, 
an E.M.F. will be generated, and current will flow magnetizing the 
shoe coils as before, but as magnetism cannot be induced in the 
setts, there will be no mutual attraction between the shoes and 
the setts, and the shoes consequently will not operate; this part 
of the braking action will therefore be useless. In this case, therefore, 
the rheostatic braking action will be the only one in operation, and 
that, as already pointed out, provided the wheels are revolving, the 
energy being spent in driving the current through the resistance in 
circuit. 

Westinghouse Magnetic Brake. — This type of brake is similar 
to the last, with the exception that when the magnetized shoes are 
drawn on to the rails, they also force brake-blocks by means 
of a suitable arrangement of levers up against the rims of the 
wheels. 

The braking action therefore, in this case, when the magnetic 
brake is applied, is threefold — 

1. A rheostatic braking action, due to the motors acting as 
dynamos. 

2. A slipper braking action, due to the friction between the 
magnetized slipper and the rails. 

3. A wheel braking action, due to the pressure of the brake-blocks 
against the rims of the wheels, this latter being brought about at the 
same time the slipper is drawn on to the rails. 

Compared with the magnetic slipper-brake just described, it will 
be seen that in the Westinghouse type an additional braking action 
is obtained by means of a wheel-brake operated as indicated. The 
braking action, of course, just as in the B.T.H. magnetic slipper, or in 
the ordinary rheostatic type of brake, can be either of a graduated, or 
of an emergency nature, as required, the emergency braking action 
being obtained by putting the power handle directly on to the last 
brake-notch. In all such cases, sand should, of course, be dropped 
while applying the brake, as it is essential the wheels should be 
kept revolving, and the sudden application might start the wheels 
skidding, in which case, of course, all three braking actions would be 
rendered useless. 



1 88 ELEMENTS OF ELECTRIC TRACTION 

The kinetic energy in this case also is ultimately converted into 
heat, just as in the previous case. 

The general behaviour, action, and advantages claimed for this 
brake are almost identical with the one just considered, and the reader 
is referred to the description given for a detailed explanation of the 
general behaviour and action. 

Application of Rheostatic or Magnetic Slipper-brake. — In 
such types of controllers as the B13 or BIS B.T.H., whether adapted 
for simple rheostatic or magnetic slipper-braking, the action of 
applying the brake is as follows : — 

If the car is travelling forward, the reverse handle then being 
in its forward position, the brake is applied in the following 
manner — . 

(1) Bring the power handle to its off position. 

(2) Bring the power handle on the brake-notches, the reverse 

handle being left in its forward on position. 
It should be noted, however, that in the case of a car ascending a 
gradient, if by any chance it should begin to travel backwards, due to 
the trolley coming off, or the power going off, the brake would have 
to be applied in the following manner — 

(1) Bring the power handle to its off position. 

(2) Bring the reverse handle to the reverse or backward position 

to correspond with the reversed motion of the car. 

(3) Bring the power handle on to the brake-notches. 
The reason for this is as follows : — 

When the motors (referring to the series motors) are employed as 
dynamos, the only field magnetism they have to rely on in starting is 
the magnetism which the field magnets retain, namely, the residual 
magnetism. The residual magnetism is generally sufficiently great 
to generate a small E.M.F., which, in turn, with a suitable resistance 
in circuit, will cause a small current to flow, and if the field-coil con- 
nections are suitable, the magnetizing effect, due to the field coils, 
will strengthen the residual field, and in this way the field will be 
gradually strengthened, or the field will be " built up," as it is termed. 
When employing the motors as dynamos, the connections are such 
that this building-up action takes place, that is, for instance, when the 
car is travelling forward and the reverse handle is in its forward 
position. If, however, the car is travelling backward, as in the case 
referred to, the motion of the wheels under these circumstances will 
be reversed, and the E.M.F. generated will send current the reverse 
way through the field coils, unless the reverse handle be operated as 
indicated. The result of this would be the residual field would be 
weakened instead of strengthened, and in this way the field would 
gradually be lost, and the dynamos under these circumstances would 
then fail to build up, and no braking action would in consequence 



BRAKES 189 

take place. By bringing, however, the reverse handle to the back- 
ward position, before placing the power handle on the brake-notches, 
the connections to the field coils will be reversed, and the reversed 
direction of current will then strengthen the residual field as desired, 
and a braking action in this way will be obtained. 

As different types of controllers vary in their construction and 
arrangement, some types being so designed as to automatically apply 
the electric brake in the event of such an accident as that described, 
the motorman cannot be too careful in obtaining definite information 
on all such points concerning the particular type he has to use. 

Motor Cut-out. — The cutting out of one motor, in most cases 
where rheostatic or magnetic slipper-brakes are employed, does not 
prevent a braking action being obtained by means of the one 
remaining motor, the retarding action, however, in this case, is less, 
being that due simply to one motor. This applies, it may be said, to 
such types of controllers as the B13, B18 B.T.H., 90M Westing- 
house, but upon all such matters the motorman should again obtain 
definite information of the particular type employed. 

Emergency Brake. — Some types of controllers are designed 
simply for emergency braking action only, and in these types con- 
sequently no graduated braking action can be obtained. Examples — 
the KIO B.T.H., and the D.E.I., form B, Dick-Kerr, are types of 
controllers designed for emergency braking only. 

In the KIO type, when the emergency stop is employed, each 
series motor is simply shortcircuited on itself, the only resistance 
then in each circuit being the resistance of the armature and field 
windings and the resistance of the various connections. 

The connections in the above case, it will be seen, are somewhat 
similar to those employed in the B18 B.T.H. rheostatic type, when 
the power handle is placed on the last brake-notch, the actual 
difference being that in the rheostatic type mentioned, the two motors 
(dynamos) are^in parallel and shortcircuited on themselves, whereas 
in the KIO emergency type each series motor (dynamo) is short- 
circuited on itself. As the resistance in each circuit is very small, a 
very powerful braking action is in this way obtained, and, as pointed 
out when dealing with the rheostatic brake, the strain thrown upon 
the motors and gearing when such braking is employed is very heavy. 
On the other hand, such powerful braking action soon stops the car, 
and consequently the excessive current due to the shortcircuiting of 
the motors now acting as dynamos does not flow for any considerable 
time, otherwise the heating effect would be serious. As it is essential 
in all emergency braking to avoid skidding, sand should, of course, be 
dropped when applying such brakes. 

In the KIO type the brake is operated by means of the reverse 
handle, there being two emergency notches provided for this purpose, 



190 ELEMENTS OF ELECTRIC TRACTION 

one in advance of the forward-running notch, and the other in the 
rear of the reverse notch. 

If the car is travelling forward, the reverse handle being in its 
forward position, the brake is applied in the following manner : — 

(1) Bring the powder handle to its off position. 

(2) Pull the reverse handle back to the far or rear emergency- 

notch, in this way passing the reverse notch. 
If the car in ascending a gradient should begin, due to some 
accidental cause, to travel backwards, the brake would be applied in 
the following manner : — 

(1) Bring the power handle to its off position. 

(2) Push the reverse handle to the front emergency notch. 

The reason for the above action is similar to that already 
described when dealing with the application of rheostatic and 
magnetic slipper-brakes. 

Motor Cut-out. — If one motor be cut out in either of the above 
types of controller, a braking action is obtained by means of the 
other motor, but the retarding force is less, being simply that due to 
one motor. 

Operating Electric Brakes. — Before concluding this part of the 
subject, it should always be remembered that the motors are acting 
as dynamos when they are employed for electric braking, and that 
the E.M.F. generated will be sending a current of more or less 
considerable value through the circuit, and, consequently, in the 
emergency type of brake, the reverse handle must not be moved 
from the emergency notch until the car has come to a standstill, 
otherwise the circuit may be broken while a large current is flowing, 
and a considerable amount of arcing may take place inside the 
controller. 

In a similar manner in ordinary rheostatic braking, the power 
handle should not be moved from the first brake-notch to the off 
position until the brake has exerted its full effect on that notch, in 
other words, until the speed has become reduced to its full extent, 
otherwise considerable arcing may take place inside the controller 
just as before, due to the breaking of the circuit when a considerable 
current is flowing. 

Regenerative Braking. — In the two regenerative systems which 
have already been described, and to which the reader is referred, the 
motors are employed as dynamos when regenerating, and the retard- 
ing action is similar to that obtained in ordinary rheostatic braking, 
the retarding effect being due to the fact that the motors are employed 
as dynamos. 

As the question of braking is also largely the question of speed 
control, there is much to be said quite apart from any question of 
economy for these systems, as in these the speed of a car can be 



BRAKES 191 

efficiently controlled over a wide range. These systems also possess 
the advantage that the retarding effect is practically in regular 
operation, and, consequently, the slightest failure is at once notified 
to the motorman. Skidding is to a large extent also reduced, as the 
motors in the ordinary way are always in actual contact with the 
trolley wire, and must therefore be either acting as dynamos and 
regenerating, or as motors, and in consequence being driven. 

Brake Combinations. — In the above descriptions the individual 
action of the various types of brake has simply been considered. 
The combination of mechanical and electrical brakes will now be 
considered. 

The majority of cars for ordinary tramway traction are fitted with 
a hand-operated wheel-brake, as well as some form of electrical 
brake. While on the one hand each brake has its own advantages 
when considered quite separately, on the other hand the combination 
of wheel-brake and electrical brake is by no means a good one. 

Combination of Wheel and Electrical Brakes. — A wheel- 
brake, as already seen, tends to lock the wheels, and, as an electrical 
brake depends entirely for its action upon the wheels revolving, if 
both brakes are operated together there is always the strong likelihood 
of the one neutralizing the action of the other. 

In some towns the use of the electric brake is limited, a motor- 
man only being allowed to use this either in emergencies, or on 
gradients which demand the use of a slipper-brake. One result of 
this is, a motorman is liable in all cases from sheer habit to turn first 
of all to the brake he is most accustomed to handling, namely, the 
hand-brake. In many cases, either due to the above habit or having 
failed to pull a car up by means of the hand-brake, he has then 
applied the electric brake, but only possibly after locking the wheels 
by means of the hand-brake. The electrical brake has in this way 
been rendered entirely useless. The proper course of action would 
have been to release the hand-brake, drop sand, and apply the electric 
brake after the wheels have regained their motion ; but the liability 
for such an occurrence as the one mentioned above is one of the 
great disadvantages and dangers of the above combination. 

While the hand-operated wheel-brake is no doubt useful for all 
ordinary work on the level, or for holding a car on a gradient, the 
ideal conditions can only be fulfilled by having some combination in 
which the action of one l3rake cannot neutralize the action of the other. 

Again, in the event of a failure of the magnetic slipper, due, say, 
to a bad or broken connection, the hand-brake is not always powerful 
enough to deal both with steep gradients and greasy rails, especially 
if the car has in any way got momentarily beyond the control of the 
driver. 

Combination of Track and Electrical Brakes. — As a 



192 ELEMENTS OF ELECTRIC TRACTION 

mechanical track-brake does not lock the wheels, the combination of 
mechanical track and electrical brake has the great advantage that 
the one cannot in this way neutralize the action of the other. On 
the other hand, as a mechanical track-brake tends to relieve the 
wheels somewhat of tlie weight of the car, the adhesive force is con- 
sequently somewhat reduced, and the driving effect of the wheels, 
and consequently of the motors acting as dynamos, is in this way 
somewhat interfered with. By limiting, however, the pressure that 
the track-brake can exert, or simply employing it as a reserve brake 
in case the electrical brake fails, the above difficulties can be over- 
come, the track-brake of itself being sufficiently powerful to deal 
with all requirements. 

At the present time, in consequence, many engineers favour the 
adoption either of a regenerative system, with some form of mechanical 
track-brake as a reserve, or some form of magnetic slipper-brake for 
regular use with a mechanical track-brake as a reserve. 

Two other methods of braking or pulling a car up by means of 
the motors will now be considered — 

1. By reversing the motors and gradually applying the power. 

2. By reversing the motors and passing into full parallel 

instantly. 

In this second method, the braking action, as will be seen in detail 
later, is due to the fact that one motor becomes employed as a dynamo, 
and supplies current to the other motor, tending to reverse that 
motor's direction. 

At the outset, it should be mentioned that the following explana- 
tions apply to those cases where, on reversing the motors, the direc- 
tion of current through the field coils is always kept the same ; that 
is, the motors are reversed by reversing the direction of armature 
current, as is the case with such types as the B13, B18, KIO 
B.T.H.; D.E.L, form B, Dick-Kerr; 90M and 210 Westinghouse. 

In cases where the fields are reversed, or where one field is 
reversed, instead of the direction of the armature current, the action 
and explanations are very similar. 

1. Reversal of Motors. — If when a car is travelling down, say, 
a slight incline, or at a fair speed on the level, the motors are 
reversed (the motorman, for this purpose, after bringing the power 
handle to the "off" position, and the reverse handle to the reverse 
position, again applies the power by means of the power handle, 
reversing the motors, that is, as far as the position of the controller 
barrels is concerned), one of two things will happen: either the 
motors will respond to the reverse action, or they will not. Whether 
they respond to the reverse action or not will depend upon the speed 
and weight of the car, or the tendency there is at work — as in the 
case of a car descending an incline — for the car to continue moving 



BRAKES 193 

in its original direction, and hence for the wheels also to continue 
revolving in their original direction. 

To reverse the motion of the motors, or, what is the same thing, 
the wheels, seeing they are geared together, the motors must first 
slow down and stop, if only for an instant, before their motion can 
be reversed. 

Responsive Action. — If now, on applying the power after 
reversing, the motors slow down, stop, and then reverse their motion 
— in other words, respond to the reversing action — the wheels will 
then reverse, and either they will slip, speeding quickly up, as they 
have very little load under such conditions, especially if the rails are 
at all greasy (the application of sand will remedy this), or they will, 
by their reversing action, pull the car up. 

The car having thus been brought to a standstill, the power 
handle should then be moved back to the *' off" position ; otherwise, an 
excessive current would then begin to flow, depending upon the notch 
the power handle happened to be on, causing the canopy cut-out in 
all probability to blow, as the car would then be starting up in the 
reverse direction, of course, with the power handle not in its starting 
position. 

In the above case it has been assumed that in the act of reversing 
the motors, namely, at the instant the motors stopped, previous to 
reversing their direction, the wheels, owing to the motion of the car, 
have not started to skid, as it must be remembered in this case 
current is passing through the motors, and so there is a force at work 
tending to turn the wheels, which if sufficiently great should prevent 
skidding, and set them in motion, namely, in the reverse direction. 
The tendency to slip, as already mentioned, however, will exist, and 
the remedy — sand. 

If the wheels skid here, as in other cases, the braking action 
will cease, or, if they slip, the braking action will in all probability 
cease to be of any value. 

If the power handle be moved from notch to notch, thus cutting 
resistance out, the motors will tend to speed up in the reverse 
direction, or if they do not speed up, there will be a greater current 
and a greater torque, and so a greater reversing or braking effect 
obtained, provided the adhesion is good — that is, the wheels do not 
slip. A too-sudden cutting out of resistance will, however, in all 
probability, start the wheels slipping. 

Non-responsive Action. — If the motors, on the other hand, do 
not respond to the reverse action, owing to the car's momentum, the 
energy stored up in the car carrying it forward, the wheels continuing 
also to revolve in their original direction in spite of all reversing 
tendencies — a car coming down a steep gradient would be very liable 
to do this — the following action will then take place : — 



194 



ELEMENTS OF ELECTRIC TRACTION 



If, just previous to reversal, the motors were being driven by 
means of the trolley pressure, and current was flowing through the 
armatures, as shown in Fig. 34, from Al to AAl, and from A2 to 



BACKE.M.F 

< 

Al r >sAAI FI 



TRoLLEy WHEFL 




El 



j^.o.i 



nsBmi 



uu 



it: 



BLOW OUT U U 
, COIL PHEOSTKTS 




J^C.0. 2 



'". *■ MJtO.S, 




FIELD \" 



HELD 
MX. 0.2, WiNDiNQ 



(ARMATUI 



^T<ly AA2 



BACK EME 



I F2V V V E2 



fTA/LS 



M.Cp.1 



777T7T 



M.C.o. RSF/fEserrrs PoiiTioN of motor CtrrouTS in ceRTAlli(K>OBrH)cafrf!OLLERS 

Fig. 34. 

AA2, then on reversing and applying the power, current will pass 
through the armature (see Fig. 35) from AA2 to A2, and AAl to Al, 

BMH EMF 



\&}vW\ 



.^»-/\ 



"^iM/uir^ 



M.C.o. I 



M.C.O S 



f£rfW 



BACK EMF. 



MCOi 



Fig. 35. 



777777 

MILS 



namely, in the same direction the back E.M.F. was previously tending 
tfo send it. 



BRAKES 



195 



As the direction of the field has not been altered, and as the 
dii-ection of rotation of the motors has not altered — the motors not 
having responded to the reverse action— the E.M.F. generated by the 
motors will still tend to send current the same way as before, through 
the armatures, namely, from AAl to Al, and from AA2 to A2. The 
result of this will be that the E.M.F. generated by the motors now no 
longer opposes but assists the trolley pressure ; an excessive current 
will in consequence flow, and the circuit breaker will be operated. 

If the car is going at a good speed when it is reversed in the way 
indicated, it will probably be found that the canopy cut-out will 
break the circuit when the power handle is moved on to the first or 
second notch after reversing. To replace it, of course, under these 
circumstances would be futile, and that brings us to the second 
method mentioned above of braking a car. 

2. Reversal of Motors. — Following the previous explanation, 



Al 




V' 



nn 



rWn 



-*. <' 



fQr'rW- 



Fig. 36. 



if, after the canopy cut-out has broken the circuit, the power handle 
be moved over to " full parallel," the connections between the motors, 
etc., will be that shown in Fig. 36. By this means a powerful 
braking action is brought about, of which the following is an 
explanation : — 

The motors, being disconnected from the trolley, can no longer act 
as motors, and on studying Fig. 36, it will be seen that the two 
motors are coupled up in parallel, but that there is no external 
circuit. If, therefore, they act as dynamos, the pressure generated by 
the one will oppose the pressure generated by the other. The reason 
for this is that as the fields were previously excited alike, the residual 
magnetic field of each will still be alike, and therefore, as both motors 
are revolving the same way, the pressure generated by each will 



196 ELEMENTS OF ELECTRIC TRACTION 

tend to send current the same way, that is, in opposition to one 
another. 

The residual magnetic field, it must be remembered, is the 
magnetism which has to be depended upon in starting a dynamo, the 
weak magnetic field due to the residual magnetism being sufficient 
to start the action. In the case of a series machine, the magnets will 
not be fully excited electrically until current flows through the 
armature circuit. 

Now, if the pressure generated by the one machine is exactly 
equal to that generated by the other, no current whatever will flow 
through the circuit, and, it may be added, no braking action of any 
kind will take place. This state of affairs is, however, not likely to 
take place, as the residual magnetic field of one motor will, in all 
probability, be not exactly of the same strength as that of the other ; 
also the speed of one motor, owing either to the wheels of one 
slipping slightly, or to one set of wheels not being exactly the same 
diameter as the other, will in all probability not be exactly the 
same as the speed of the other. The result is that one dynamo will 
in all probability generate a slightly higher pressure than the 
other. 

If No. 1 machine generates a slightly higher pressure than No. 2, 
as the pressure generated will tend to send current the same way the 
back E.M.F. did previously, a small current, depending upon the 
difference of pressures generated, will flow from AAl to Al, from Fl 
to El, from E2 to F2, from A2 to AA2, and from AA2 to AAl. The 
current passing through the field of No. 2 in the reverse direction 
will weaken its residual field, causing a lesser pressure to be generated 
in that machine, and a greater current in consequence to flow. In 
this way No. 1 machine will gradually build up as a dynamo, and 
will force current through the field of No. 2 machine in the reverse 
direction, thus reversing the field, but, owing to the reverse con- 
nections, the current will still pass through the armature of No. 2 
machine in the same direction as originally — that is, when driven by 
means of the trolley pressure. Eeversing the field and keeping the 
direction of the armature current the same, means that No. 2 will 
endeavour, as a motor, to reverse its direction. The whole effect 
summed up is, that if No. 1 is on the front wheels, and No. 2 on the 
rear wheels of the car, No. 1, acting as a dynamo, will tend to stop 
the motion of the front wheels, and No. 2, acting as a motor, with its 
direction reversed, will not only tend to stop the rear wheels, but also 
tend to reverse their motion, and so the direction of the car, the 
whole bringing about a powerful braking effect. 

If for any reason an electric brake fails to act, there is at hand in 
the above method an emergency means of braking the car indepen- 
dent of the ordinary electric brake. 



BRAKES 197 

When once the circuit breaker has broken the circuit, of course 
no pressure is available for reversing a car in the ordinary way, and 
if the above method is to be adopted, the power handle should then 
be moved into full parallel at once. If by one of those peculiar 
circumstances the above failed to act, that is, if the dynamos did 
happen to generate exactly equal pressures, then the breaking of the 
circuit and the making of it again by means of the power handle 
would in all probability upset such delicate equilibrium, and bring 
about the desired effect. 

If desired, before applying power after reversing by means of the 
reverse handle, the circuit breaker could be "tripped" by hand, 
instead of allowing it to come out automatically. In emergency 
cases, tripping the circuit breaker by hand in this way is possibly the 
quickest and surest plan to adopt, the power handle then being 
placed into full parallel immediately — that is, after placing the 
reverse handle, if this has not already been done, in its correct position. 

Summing up, it will be seen that the above braking action takes 
place when the trolley circuit is broken by means of the circuit 
breaker or canopy cut-out — assuming the trolley is still on — and in 
the event of the car travelling forward the handles being placed in 
the following position : — 

Eeverse handle in the rear reverse position ; 
Power handle on full parallel ; 
or, if the car is travelling due to some accidental cause backward 
down a gradient, the handles being placed in the following position, 
circuit breaker being tripped as before : — 

Eeverse handle in the forward position ; 
Power handle on full parallel ; 
the reverse handle in each case, it will be noted, being in the reverse 
direction to that of the car's motion. Application of sand here, as in 
other cases of electrical braking, is essential, as the whole of the 
action depends upon the rotation of the wheels. 

Motor Cut-out. — In the event of one motor being cut-out, no 
braking action would of course take place. 

It should also be noted that had the canopy cut-out been 
"tripped" so as to disconnect the trolley pressure, and the motors 
(neither being cut out) put in parallel without reversing, that is, 
when the car is travelling forward, no braking action would have 
taken place. In this case, neither machine would build up as a 
dynamo, as will be seen on studying Fig. 37. If No. 1 machine 
generates, due to residual magnetism, a higher voltage than No. 2, 
current would then tend to flow from AAl to Al, from A2 to AA2, 
from r2 to E2, and note from El to El. The E.M.F. generated 
in No. 2 machine would, of course, tend to send current in the reverse 
direction to this. 



198 



ELEMENTS OF ELECTRIC TRACTION 



It will now be seen there are two causes at work tending to 
reduce this small initial current passing through the circuit. 
First, the E.M.F. generated by No. 2 is opposing that of No. 1, and, 
secondly, the direction of current through the field of No. 1 — now 
acting as a dynamo — is such as to weaken its own residual field, 
being in the reverse direction. The consequence is, No. 1 will fail to 
build up as a dynamo, the small pressure generated due to the 
residual field getting less and less as this becomes weakened, and 
finally both motors will cease to operate entirely either as motors or 



AI/''">sAM Fl 



El 



^v 



l^n 



m 



ru": 




fcQ-«?-5%£ 



TTrtTTJ 



Fig. 37. 



dynamos. In the event of a car travelling backward, no braking 
action would take place if the reverse handle was placed in the rear 
reverse position, this position of the reverse handle being really the 
correct one for running the car backward if so desired, and hence not 
the reverse position for this particular direction of motion, the forward 
position being the reverse position for the backward direction of 
motion. 

While dealing with the above method of braking, it may be said 
that when series dynamos have to be coupled in parallel to supply 
an external circuit, a similar difficulty arises in getting the two 
dynamos to give exactly the same pressure, and to overcome this, 
a connection is generally made from the armature of one dynamo 
to the armature of the other, namely, from C to D. See Fig. 38. 

This cross-connection provides a path so that current is able to 
flow from the armature of the machine with the higher pressure 
across to and through the field of the machine generating the lesser 
pressure, and in this way, by means of this connection, the field of 
the weaker machine is strengthened. The pressures in this way are 



BRAKES 



199 



automatically adjusted until they become equal, which enables the 
dynamos to be run in parallel. Such cross-connections, or their 
equivalent, will be found to exist wherever series dynamos are run 
in parallel, as, for instance, when they are arranged for rheostatic 
electric braking. See Fig. 33. 

In some of the Dick-Kerr controllers, each motor, when acting as a 
dynamo, excites the other's field, and the cross-connection referred to 
above is in this way dispensed with in this particular arrangement. 

Finally, with regard to all braking, with the speeds that are now 
adopted — or sometimes attained — in electric tramway traction, it 
is essential that no time should be lost by the motorman in all 




AAAAAAAAAMAA 



Fig. 38. 



emergency cases in effectively applying the brakes. The need for 
prompt action will be more apparent when it is remembered that a 
car travelling at 10 miles an hour covers a distance of some 15 feet 
every second, and at a speed of 20 miles a car will travel some 30 
feet — in this case practically its own length — every second. It is 
therefore essential that a motorman should know beforehand exactly 
what to do in the event of any emergency, and for this purpose 
should be carefully instructed in the working of the various types of 
controllers he has to handle. Where brakes are not in regular use, 
not only should daily examination be made of these, but opportunities 
should at least be given the motorman for obtaining the necessary 
skill and confidence in the use of all braking apparatus. 



200 ELEMENTS OF ELECTRIC TRACTION 



Examples 

(1) An 8 -ton car is travelling at a speed of 10 miles per hour. 

(a) What is the value of the kinetic energy in foot-tons stored up 
in the car under these conditions ? 

(h) If in reducing the speed of the car 60% of the above energy 
is regenerated, what will be its value expressed in B.O.T. units ? 

(a) As kinetic energy (K.E.) in foot-tons = -^^ approximately, 

,\ K.E. = ^ = ^oQqO- = approximately 2 6 6 foot-tons 

Therefore kinetic energy stored up in the moving car = 26-6 foot- 
tons. 

(b) As 60% of the kinetic energy is assumed to be regenerated, 

.*. energy regenerated = 2 6 '6 x ^^qq = 15*96 foot-tons ap- 
proximately. 

As 1 B.O.T. unit = 1000 watt hours, and as 746 watts = 1 
E.H.P., 

.-. 1 B.O.T. unit = i^£^- = approximately 1-34 E.H.P. hours. 

Energy supplied at the rate of ^f^£ E.H.P. for 1 hour 
= \%^ X 33,000 X 60 foot-lbs. 
= 2,654,155 foot-lbs. approximately 
= 1184-89, say 1185 foot-tons 
= 395 yard-tons approximately 
.•. 1 B.O.T. unit is equivalent to 1185 foot-tons 
In other words, if 1185 foot-tons of mechanical energy were 
all converted into electrical energy it would be equivalent to 
1 B.O.T. unit. 

15*96 
.-. energy regenerated is equivalent to = 0-013 B.O.T. unit 

Therefore energy regenerated in above case would be equivalent 
to 0-013 B.O.T. unit. 

In dealing with problems similar to above, it is useful to re- 
member that in supplying power, 1 B.O.T. unit is equivalent, with 
an efficiency of conversion of 85%, to approximately 1000 foot-tons, 
and that in regenerating at an efficiency of 85%, 1400 foot-tons of 
energy are approximately equivalent to 1 B.O.T. unit. 



BRAKES 201 

(2) An 8-ton car starting from rest descends a gradient of 
1 in 17-5. 

Assuming a tractive resistance of 25*4 lbs. per ton — 

(a) What speed will the car attain in 10 seconds ? 

(h) What number of yards will it travel in the 10 seconds ? 

(c) How much of its potential energy will have been expended ? 

(d) What would be the value of the car's kinetic energy at the 
end of the 10 seconds ? 

2240 
(a) Gravitational pull per ton weight = y^ttf = 128 lbs. 

Tractive resistance per ton weight = 25 '4 lbs. 
.'. accelerating force per ton weight = 128 — 25'4 = 102*6 lbs. 

As 102*6 lbs. per ton will give to the car an acceleration of 
1 mile per hour per second, 
.*. in 10 seconds the car will attain a speed of 10 miles per hour. 

Therefore speed attained in 10 seconds = lo miles per hour. 

(b) Average speed during the 10 seconds, as the acceleration has 
been constant — 

= 5 miles per hour 

1760 X 5 , 
= ocf)r) — yards per second 

.'. distance travelled in 10 seconds = ttttt^ 

ooOO 

= 24-44 yards = 73-32 feet 

Therefore distance travelled during the 10 seconds = 24-44 
yards. 

The distance travelled could also have been calculated from the 
formula — 

AT 

4-09 

(c) Vertical height descended by car = ?^ = 1*39 yards 

= 4-17 feet 
.*. potential energy expended = 2240 x 8 x 4-17 

= 74,726-4 foot-lbs. 

Therefore potential energy expended during the 10 seconds = 
74,726-4 foot-lbs. 



202 ELEMENTS OF ELECTRIC TRACTION 

{d) The car's kinetic energy will equal the potential energy 
expended, less that required for overcoming tractive resist- 
ance. 
Energy expended in overcoming tractive resistance = 25*4 X 8 

X 73-32 = 14,898-624 foot-lbs., 
.'. kinetic energy possessed by the car at tlie end of the 10 
seconds = 74,726-4 - 14,898-624 = 59,827-77 foot-lbs., ap- 
proximately = 26-7 foot -tons 
Therefore kinetic energy stored up in the moving car at the end 
of the 10 seconds = 26-7 foot-tons approximately. 

Note. — This same result could have been obtained by calculating 
the kinetic energy direct from speed and weight of moving car. 
See previous example, and compare. The two results would be 
found to agree exactly if calculations were worked out more 
accurately. 

(3) A car starting from rest descends a gradient of 1 in 1 2. 

Assuming a tractive resistance of 25 lbs. per ton — 

{a) What number of yards would the car travel in 5 seconds ? 

(&) What number of yards would the car travel in attaining a 
speed of 15 miles per hour ? 

This problem could be worked out from first principles similar 
to the above. As the tractive resistance is assumed, however, to be 
25 lbs. per ton, it can be more readily calculated from the approximate 
formulae — 

S=(90-G)t and ^^ = Y^^^ 
4G G 



Thus— 

/^ A.Q (90 -G) 

(a) As S = — ^^ i 

. . . r 1 90 -12 ... , 

speed attamed m 5 seconds = j^rrjo -^ 1 ~ 48 ^ 48 

= 8-125 miles per hour 

(90 - G) 



4G 
90-12 5 78 . 390 



And as S2 = Y 



G 



.-. 8125 X 8-125 = y(90 " l^) 



12 



78Y 
.-. 66 approximately = -zr^ 



Y = — =-^ — = 101 yards approximately 

7o 



BRAKES 203 

Therefore distance travelled in the 5 seconds = lo-i yards 
approximately. 

The above two approximate formulae can easily be combined, and 
the result is that — 

(90 -G) 
16G 

This enables the above result to be more readily calculated. 
Thus— 

_ (90 - 12) _ 78x25 _ 
^ ~ 16 X 12 192 ~ '■"^ ^^ ''"°'^^ 



(*) 



AsS^ = y(50-G) 
• • ~ (90 - G) 



. . ,, , 15 X 15 X 12 2700 .,, . 
.-. yards travelled = ^^ __ ^^ = -^ = 34-6 

Therefore distance travelled in attaining a speed of 15 miles per 
hour = 34-6 yards. 

(4) What speed would a car attain in travelling 50 yards down a 
gradient of 1 in 12, if it commences to descend the gradient at a 
speed of 2 miles per hour, assuming the tractive resistance to be 
25 lbs. per ton ? 

Answer — 

20 miles per hour approximately. 

(5) What gradient would be necessary so that a car, in descending 
such without the aid of the motors on the one hand, and without the 
application of the brakes on the other, would just maintain a speed 
which has previously been given to it, on the assumption that the 
tractive resistance for that speed is 17 lbs. per ton ? 

Answer — 

1 in 131-7 



(6) A car travelling at 25 miles per hour is pulled up by means 
of an emergency brake in 4 seconds. 

(a) What is the average value of the retardation expressed in 
miles per hour per second ? 

(h) What number of yards will the car travel in the 4 seconds if 
the retardation is of constant value ? 



204 ELEMENTS OF ELECTRIC TRACTION 

Answer — 

(a) 6J miles per hour per second. 
(h) 25 yards approximately. 



(7) A car travelling at 14 miles per hour on the level is pulled 
up by means of an emergency brake in 5 J yards. 

(a) Assuming the retarding force has been of constant value, 
what is the value of the retardation expressed in miles per hour per 
second ? 

(h) What is the time taken in seconds to stop the car ? 
Ansiver — 

(a) 8"7 miles per hour per second. 
ih) 16 seconds approximately. 



(8) An 8-ton car is travelling at a speed of 6 miles per hour. 
Assuming a tractive resistance of 20 lbs. per ton — 

(a) How far would the car travel on the level if no brakes of any 
kind were applied ? 

(b) How far would it travel up a gradient of 1 in 20 if no brakes 
were applied ? 

(a) As kinetic energy in foot-lbs. = WS^ x Tf) approximately, 
.-. K.E. stored in car = 8 x 6 x 6 x 75 = 21,600 foot-lbs. 
approximately. 

Eetarding force due to friction = 20 x 8 = 160 lbs. 

As K.E. in this case is expended simply in overcoming frictional 
resistance, and as work done in foot-lbs. in overcoming 
frictional resistance = 160 lbs. x distance travelled in feet, 

.*. K.E. in foot-lbs. = 160 lbs. x distance travelled in feet, 

.-. 21,600 „ = 160 lbs. X 

•'• -Mu"^ >> = distance travelled = 135 feet. 

Therefore the distance the car would travel = 135 feet. 

Note. — A rough rule (which is based on an assumption of a 
tractive resistance of 25 lbs. per ton) is that the (speed in miles per 
hour)^ = yards travelled on the level without brakes of any kind. 

(&) Eetarding force due to friction =160 lbs. 

8 X 2240 
Retarding force due to gravitation = — ^ = 896 lbs. 

Total retarding force = 1056 lbs. 

.-. distance travelled = ^^S>^~ = 20*45 feet 



BRAKES 205 

Therefore the distance the car would travel up the gradient 
= 2045 feet approximately. 

(9) A 10-ton car, fitted with two motors and wheels 30 inches 
diameter, in descending a gradient of 1 in 13 at a speed of 25 miles 
per hour is pulled up by means of an emergency brake in 25 yards. 
Assuming the tractive resistance is 22 lbs. per ton — 

(a) What is the average retarding draw-bar pull exerted by the 
motors during the time the car is being stopped ? 

(h) What is the average retarding torque exerted by each motor 
on the driving axle during that time ? 

The average retarding draw-bar pull can be calculated, knowing 
the distance the car travels in being pulled up, and the tractive 
resistance, from the kinetic energy the car possesses and the potential 
energy expended on the car. 

Assuming, on the other hand, that the retarding force is of 
constant value, it can be calculated as follows : — 

g2 

(a) . As A = -jy approximately 

Ketardation = -^ — ^ = 6j miles per hour per second approx. 

As 102*6 lbs. per ton are required to give an acceleration of 

1 mile per hour per second, 
So also 102"6 lbs. per ton are required to give a retardation of 

1 mile per hour per second. 
.*. to give above retardation, the retarding force required per ton 

= 102-6 X 6-25 = 641-25 lbs. 
.*. to give above retardation, retarding force required 

= 641-25 X 10 = 6412-5 lbs. 

Ketarding di^aw-bar pull required to balance gravitational effects 

10x2240 ,^00 -.1 
= ^ = 1723 lbs. 

Frictional retarding force = 22 x 10 = 220 lbs. 
As friction assists in retarding the car, 
.*. nett retarding draw-bar pull = 6412*5 -}- 1723 - 220 lbs. 

= 7915*5 lbs. approximately 

Therefore average retarding draw-bar pull exerted by the motors 
under above conditions = 79i5'5 lbs. approximately. 

(h) Average retarding draw-bar pull exerted by each motor 

= "^i^'^ = 3957-7 lbs. 



2o6 ELEMENTS OF ELECTRIC TRACTION 

With driving wheels 30 inches diameter, or 1-25 feet radius, 
average retarding torque exerted by each motor 
= 39577 X li = 4947 Ibs.-feet approximately 

Therefore average retarding torque exerted by each motor on the 
driving axle = 4947 Ibs.-feet approximately. 

(10) A 10-ton car fitted with two motors and wheels 30 inches 
diameter is ascending a gradient of 1 in 50 at a speed of 10 miles 
per hour, and is pulled up by means of an emergency brake in 4 yards. 
Assuming a tractive resistance of 22 lbs. per ton — 

(a) What will be the average retarding draw-bar pull exerted by 
the motors ? 

(b) What will be the average retarding torque exerted by each 
motor on the armature shaft, the gear ratio being 4' 5 to 1. 

Answer — 

(a) 5744"5 lbs. approximately. 
(h) 797'7 Ibs.-feet approximately. 

(11) A 10-ton car is descending a gradient of 1 in 10 at a speed 
of 20 miles per hour, and is slowed down by regenerative control to 
10 miles per hour in 100 yards. Assuming that under the above 
conditions the dynamos have an efficiency of 70%, and that the 
tractive resistance is 25 lbs. per ton, what will be the value of the 
B.O.T. units restored ? 

WS^ 
As kinetic energy in foot-tons = -^^r approximately 

.*. K.E. possessed by car when travelling at 20 miles per hour 
10 X 20 X 20 



30 



= 133*3 foot-tons approximately 



As the car descends a vertical height of 10 yards or 30 feet 
in travelling 100 yards down the gradient. 

Potential energy expended on car during that time 
= 10 X 30 = 300 foot-tons 

Energy expended in overcoming tractive resistance 

25 X 10 X 300 ooA^^. 

= fSTTTT^ — - — = 33*4 loot-tons 

2240 

K.E. possessed by car when travelling at 10 miles per hour 

_ _ — = 33-3 foot-tons 



BRAKES 207 

Initial K.E. and potential energy expended on car 
= 133-3 + 300 = 433-3 foot-tons 

Final K.E. and energy expended in tractive resistance 
= 33-3 + 33-4 = 66-7 foot-tons 

.*. total energy absorbed in slowing down 

= 433-3 - 66-7 = 366-6 foot-tons 

With dynamo working at an efficiency of 70%, energy regenerated 
= 366-6 X xm) = 256-62 foot-tons 

Equivalent value of energy regenerated 
256-62 



1185 



= 0-2ia B.O.T. unit 



Therefore the value of the electrical energy regenerated = 0*216 
B.O.T. unit. 

(12) A 10-ton car is maintained at a speed of 4 miles per hour 
for a distance of 200 yards in descending a gradient of 1 in 13 by 
regenerative control. Assuming the dynamos under these conditions 
have an efficiency of 60%, and that the tractive resistance is 22*4 lbs. 
per ton — 

(a) What would be the value of the B.O.T. units regenerated ? 

(b) Assuming the voltage at the terminals of the dynamos is 
520 volts, what would be the value of the current sent back to the 
line? 

(a) Vertical height descended by car = ^^- = 15*38 yards 

= 46-14 feet 

.*. Potential energy given to car in travelling 200 yards 
= 10 X 4614 = 461*4 foot-tons 

Energy expended in overcoming tractive resistance 
22-4 X 10 X 200 X 3 



2240 



= 60 foot- tons 



.*. Energy delivered to dynamos = 461*4 — 60 foot-tons 

= 401*4 foot-tons 

With an efficiency of 60%, energy regenerated 
= 401-4 X -fo^o = 240-84 foot-tons 



2o8 ELEMENTS OF ELECTRIC TRACTION 

Equivalent value of electrical energy in B.O.T units 

= ,^^ = 0-203 B.O.T. unit 
1185 

Therefore the value of the electrical energy regenerated = 0-203 
B.O.T. unit. 

(b) A rate of 4 miles per hour is equivalent to a rate of 7040 yards 
per hour 

.*. time taken to travel the 200 yards = w7vtf\ = tt^^-t^ tour 

'^ 7040 35'2 

0-203 B.O.T. unit = 203 watt hours 

.*. watts supplied during ^^hour = 203 x 35-2 

= 7145-6 watts 
As pressure at terminals = 520 volts 

7145-6 . ^ ^ 
.*. current m amps. = ^^^ = 13 7 amps. 

Therefore value of the current restored to line during the time 
considered = 137 amps. 

(13) A 10- ton car travelling at a speed of 20 miles per hour on 
the level is slowed down by regenerative braking to 10 miles per 
hour in 100 yards. Assuming the dynamos under these conditions 
have an efficiency of 70%, and that the tractive resistance is 25 lbs. 
per ton — • 

What would be the value of the B.O.T. units restored ? 
Ansiver — 

0-0393 B.O.T. unit 

(14) Assuming the maximum adhesive force between wheels and 
rails is 400 lbs. per ton, and the tractive resistance is 25 lbs. per ton, 
what is the shortest distance a car can be pulled up in under these 
conditions on the level at any given speed when rheostatic braking is 
simply and solely employed ? 

As maximum adhesive force is 400 lbs. per ton, 

.'. maximum retarding draw-bar pull motors can exert when 

acting as dynamos = 400 lbs. per ton. 
Resistance to traction = 25 lbs. per ton. 
Kinetic energy stored in car = S^ X 75 approx. foot-lbs. per 

ton. 



BRAKES 209 

As K.E. is expended in overcoming tractive resistance and 
retarding draw-bar pull due to the motors acting as 
dynamos, 

.*. K.E. in foot-lbs. = total resisting force in lbs. X distance 
travelled in feet. 

.-. S2 X 75 = 400 4- 25 X feet travelled. 

/. distance travelled in feet = -tf^ — = c 7.7^ 

425 5-66 

Therefore under above conditions the shortest distance in feet a 
car can be pulled up in on the level is obtained by dividing the 
square of the speed in miles per hour by 5 '66. 

A rough rule is to divide the square of the speed in miles per 
hour by 6. The above example indicates what is the shortest 
distance a car can be pulled up in on the level by rheostatic braking 
under what is practically the best condition of rails. The use of 
sand increases the adhesive force, and hence enables the distance as 
calculated above to be reduced. 



INDEX 



[Numbers in italics refer to pages of examples on the subject.} 



Acceleration, 88, 113 

and speed, 88, 90, 108-111, 112, 117, 
161, 175, 201, 202, 203 

conditions requisite, 90, 108, 109, 110, 
144 

constant, 91, 108, 110, 111, 159 

equivalent values, 89 

formulae, 92, 175 

value depending on, 91, 92, 109, 110, 
111 

with given gradient, 97, 117, 201, 202, 
203 
Accelerating force, 90, 96, 97, 112, 114, 
201 

and speed, 109, 175 
Adhesive force, 104, 192, 193, 203 
Alternating current, 48 
Alternator, simple, 48 
Ammeter, 23, 25, 34 
Ampere, 21 

hour, 72 

turns, 16, 17, 18, 51 
Arcing inside controller, 190 
Armature, 

conductors, 52 

conductors' pull on, 55, 58 

core, 51 



B 



Back E.M.F., 40, 60, 65, 66 

value depending on, 62 
Balance of forces in traction, 108, 110, 
111, 144, 159, 160 
torques, 76 

torques in motor, 121, 133, 
135, 136 
Blow-out coil, 5, 156 
Board of Trade panel, 3 
Board of Trade Regulations, 
brakes, 177 

current density in rails, 31 
drop in rail return, 30 



Board of Trade Regulations — contd., 

trolley-wire pressure, 1 

trolley- wire sections, 3 
Board of Trade unit, 72, 82, 83, 84, 163, 

200, 206, 207, 208 
Bonding of rails, 31 
Brakes, 

air-operated, 176, 179, 180 

application of emergency, 189 
rheostatic, 188 

automatic, 168, 170, 189 

classification of, 176 

combination of, 177, 191 

electric, 176, 180 

electro-magnetic, 176, 185, 187 

emergency, 189 

function of, 171 

hand, 176, 177, 178, 179, 182, 191 

magnetic slipper, B.T.H., 185 
Westinghouse, 187 

notches, 183 

on gradient, 171, 183 

operating electric, 190 

rheostatic, 176, 183 

track, 176, 177, 179, 185, 187, 191 

wheel, 176, 177, 187, 191 
Braking, 

action with one motor, 189, 190, 197 

advantages of electric, 183 

bv reversal of motors, 192, 195 

electric, 156, 180, 190 

emergency action, 177, 184, 186, 187 

examples on, 203-208 

general principle, 171 

regenerative, 164, 176, 190 

retarding force in electric, 176, 180, 181, 
182, 183, 186, 190, 191 

retarding force in mechanical, 178, 179 

rheostatic, 163, 168, 184, 187 
Brake Horse Power, 73, 82, 83, 106, 141 

and current, 76, 82, 86 

and torque, 79, 85, 106, 114, 123 

measurement of, 74, 75, 106 
Brushes, 48, 51 
Bus bars, 2, 3 



212 



INDEX 



c 



Cables, 37, 86, 142 

Canopy cut-out, 3, 5, G, 38, 193, 195, 197 
Car equipment, 3 
Car mile, 82, 84, 163 
Car on level, 108, 109 
gradient, 110 
Centrifugal force, 118, 134 
Characteristic properties, 52, 118 

compound cumulative motor, 119, 138 
differential motor, 119, 138 
dynamo, 53, 54 

separately excited dynamo, 51 

series dynamo, 53, 54 
motor, 118, 127 

shunt dynamo, 52, 53 
motor, 118, 125 
Chemical effect, 20, 25 
Choking coil, 5, 6 
Circuit breaker, automatic, 1, 2, 3, 5, 6, 7, 

38, 193, 195, 197 
Circumference, 75 
CoeflBcient of friction, 93 
Commutator, 49, 50, 59 
Compound, 

dynamo, 51, 54 

motor, cumulative, 119 
differential, 119 
Conductors, 

and non-conductors, 22 

armature, 52, 55, 58 

in magnetic field, 5G, 58 
Connections, terms employed, 31 
Conservation of energy, 67 
Contact surfaces, 37 
Continuous current, 49 
Controller, 

arcing inside, 190 

barrels, 156 

blow-out coil, 5, 156 

diagram of connections, 155, 194, 195, 
198 

functions of, 154 

handles, interlocking of, 64, 156 

motor cut-outs, 157, 189, 190, 197 
Controller operations, 157 

paralleling, early, 162 

late, 160, 162 

passing into full parallel, 159 
full series, 158 

running on full series, 160 
Controller types, 

B.T.H. B13..64, 156, 157, 184, 188, 
189 192 

B.T.H. B18, 5, 156, 157, 184, 188, 189, 
192 

B.T.H. K2, 153 

B.T.H. KIO, 156, 157, 189, 192 

Dick-Kerr D.B.I., 156, 157, 184 

Dick-Kerr D.E.I., 189, 192 



Controller types — contd., 

Westinghouse 90M., 156, 157, 189, 192 

Westinghouse 210.. 156, 157, 192 
Coulomb, 21, 70, 72 
Cumulative winding, 119 
Current of electricity, 20, 21 

alternating, 48 

complete circuit for, 3, 20, 48 

conditions for flow of, 20 

continuous, 49 

density in cables, 37, 86 
rails, 31 

effects due to, 20, 23, 24, 25 
Curves of magnetization, 18 
Cut-outs, 

automatic. See Circuit Breaker 

motor controller, 157, 189, 190, 197 



D 



Demagnetizing action, 54, 125 

effects in dynamos, 54 
motors, 141 
Derailed car, 179, 187 
Diagram of, 

car circuit, 4 

controller connections, 155, 194, 195, 198 

traction circuit, 2 

motor test, 131, 132, 145, 146 
Dielectric, 22 

Difference of potential, 21, 39, 40 
Differential winding, 119 
Direction of current, 31 

test for, 14 
Distinction between, 

distance, speed, and acceleration, 90 

force, energy, and power, 70 

load and power, 123 

torque and power, 123 
Distribution, general principle, 1 
Draw-bar pull, 90, 97, 99, 114, 116, 117, 
143, 205, 206 

and B.H.P., 98, 106. 114, 116 

and current, 103, 108, 116, 143, 147, 150, 
152 

and load, 123, 144 

and torque, 102, 106, 114, 117, 205, 206 

formulae, 106, 107, 108 

measurement of, 105 

under varying conditions, 108, 109, 110, 
111,144, 147,150, 152 

value varying with, 103, 143, 147, 150, 
152 

with series motors, 145-162 

with shunt motors, 151, 166 
Driving force in motor, 58 
Drop, 29, 39, 40, 41 

in armature, 30, 54 

in batteries, 30, 39, 40 

in cables, 37, 142 

in rail return, 30 



INDEX 



213 



Dynamo, 

E.M.F. value, 44 

E.M.F. and P.D., 30, 54 

essential features, 44 

in parallel, 32, 33, 156, 198 

magnetically considered, 180 

polarity of, 14, 31 

principle of, 43 

right-hand rule, 45 

simple, 47 

types of, 51 
Dynamo, characteristic properties of, 52 

compound, 53, 54 

separately excited, 51 

series, 53, 54 

shunt, 52, 53 



E 



Earth a conductor, 23 
Earth switch, 3, 7, 32 
Earth wire, 5 
Earthed return, 3 
Earth's magnetism, 10 
Eddy currents, 52 

eflfects due to, 142 

loss due to, 140 
Efficiency, 72, 76, 82, 83, 86, 116, 117, 

200, 206, 207, 208 
Electricity, 

conditions for flow, 20 

conductors and non-conductors of, 22 

current, pressure, and quantity of, 21 

generator of, 21 

resistance to flow, 21 
Electrolysis, 25, 31 
Electromotive force, 30 

and P.D., 30, 39, 40, 54 

back, 40, 60, 62, 65, 66 

of dynamo, 44 
Electro-magnet, 12, 16, 19, 51, 176, 185 
Electro-magnetism, 14 
Energy, 67, 82, 83 

conservation of, 67 

consumption of, 82, 84, 163 

conversion of, 68, 99, 110, 112, 162, 171, 
172, 186, 188 

converted in motor, 123, 138, 139, 141 

electrical, 70, 82, 83, 84, 163, 200, 206, 
207,208 

expended in traction, 90, 162, 171 
Energy, kinetic, 99, 171, 173, 200-208 

calculation of, 98, 173, 174, 175 

conversion of, 110, 112, 172, 186, 188 

recovery of, 162, 200, 206, 208 
Energy, potential, 99, 112, 117, 162, 16:-, 
171, 172, 201, 205, 206, 207 

recovery of, 117, 162, 172, 206, 207 
Excitation of field, 51, 118 
Examples, 39, 65, 82, 112, 200 . 



F 



Feeder 

boxes, 3 

cable and panel, 2 

return, 31 
Field, 

building up of, 53, 55, 188, 194, 196, 198 

changing device, 164, 170 

circuit, making and breaking, 137, 145 

coils and magnets, 31, 51, 53, 188 

excitation of, 51, 118 

intensity, 17, 55, 58, 124, 125 

magnetic, 11 

residual, 53, 54, 188, 195, 196, 198 
Field strength, 

efiects of varying, 53, 131, 133 

weakening, 119, 128, 131, 133 

method of varying, 53, 125, 135, 165 
Flow of electricity, 20 
Flux, magnetic, 17 
Foot-lbs. of work, 67, 71, 82, 83 

and H.F., 69, 70 
Formula, 28, 92, 96, 106, 107, 108, 139, 

173, 174, 175 
Friction, 92 

coefficient of, 93 

effects of, in traction, 109, 110, 111 

energy expended in, 68, 94, 98, 99, 110, 
112, 162, 171,202-208 

rolling, 94 

sliding, 92, 94 

value varying with, 93 
Frictional losses in motor, 138, 140 

resistance to traction, 94, 95, 
114, 116, 143, 201-208 
Fuses, 38 



G 



Gearing, 100 

Gear ratio, 100, 103, 114, 206 
Generator, electric, 21 
Gradient, 96 

for given acceleration, 97 

speed attained on given, 97, 117, 174, 
201, 202, 203 

work done in mounting, 96, 98, 99 
Gravitational force, 95, 96, 98, 112, 114, 
116, 117, 201 

H 

Heat, 

generated in braking, 110, 112, 172, 176, 

178, 180, 185, 186, 188 
generated in traction, 99, 110, 112, 162, 

171 
quantity and temperature, 24 
Heating effects, 

in dynamo and motor, 63, 70, 123, 138, 
142, 185, 186, 189 

p 3 



214 



INDEX 



Heating effects — contd., 

of a current, 20, 23, 32, 176 

watts expended in, 84, 139 
Horse-power, 69 

and watts, 71, 82 

brake, 73, 74, 79, 82-86, 106, 114, 141 

electrical, 71, 72, 76, 82, 83, 86, 117 

expended in traction, 98, 106, 107, 108, 
114, 116 

load and torque, 123 
Horizontal effort, 100, 102, 143 
Hysteresis, 13 

effects due to, 142 

loss due to, 140 



Incandescent lamp, 24, 39 
Inductive windings, 137 
Input of motor, 

measurement of, 72 

self-regulation, 119 
Instruments, measuring, 23, 25, 34, 72 
Insulating materials, 23 
Insulators, 22 



JoHNSON-LuNDELL regenerative system, 

165, 167, 168 
Joule, the, 70 



K 



Kilowatt, the, 71, 72 

Kinetic energy, 99, 171, 173, 200-208 
calculation of, 98, 173, 174, 175 
conversion of, 110, 112, 172, 186, 188 
recovery of, 162, 200, 206, 208 



Lamination of armature core, 52 
Late paralleling, 160, 162 
Leakage, magnetic, 14 

to trolley standard, 7 
Left-hand rule, 59 
Lighting of car, 8 
Lightning arrester, 3, 5 

action of, 6 
Lightning discharge, 6 
Lines of force, 13 
Live wire, 7, 8, 20 
Load and power, 123 
Losses in motor, 138 

M 

Magnet, 
bar, 9 

electro-, 12, 16, 19, 51, 176, 185 
poles, 10 



Magnet — contd., 
permanent, 12 
properties of, 9 
Magnetic, 
attraction and repulsion, 9, 10 
blow-out, 5, 58, 156 
circuit, 18 

effects due to a current, 14, 56, 58 
field, 11 
flux, 17 
force, 11, 13 
hysteresis, 13, 140, 142 
induction, 10, 11, 16, 185 
leakage, 14 
lines of force, 13 
materials, 9 
permeability, 16 
polarity, 11 
retentivity, 12 

saturation, 17, 54, 130, 137, 148, 166, 186 
screening, 19 
Magnetism, earth's, 10 
electro-, 14 

residual, 12, 53, 54, 186, 188, 196, 197 
theory of, 13 
Magnetization, curves of, 18 

methods of, 12 
Magnetizing force, 16, 18, 124 
Megohm, 22 
Milliampere, 89 
Motor, continuous-current, 
action of, 80 
analysis, 124 

back E.M.F., 60, 62, 65, 66 
constant-speed, 119 
construction of, 58 
controller cut-outs, 157 
driving force in, 58 
effective H.P. and torque, 141 
energy converted in, 123, 138, 139, 141 
essential features, 57 
left-hand rule for, 59 
load and power of, 123 
load-limiting factors, 142 
losses, 138 

main switch for, 5, 63 
measurement of, 

brake H.P., 74, 75, 106 
input, 72 
principle of, 56 
simple, 61 
starting of, 62 
Motor, 
test of series, 75 

traction, 131, 132, 145, 146 
torque of. See Torque 
Motors, continuous-current, 
characteristic properties of, 
compound, 119, 138 
series, 118, 127 
shunt, 118, 125 



INDEX 



215 



Motors, continuous-current — contd., 
classification of, 118 

compound, 119 

series, 118, 127, 145-162 

shunt, 118, 125, 151, 166 
efifects due to, 

field variation in, 131, 133 

pressure variation in, 131, 135 

secondary actions in, 141 
in parallel, 151, 152, 153, 154, 159, 160, 

195, 197 
in series, 151, 152, 153, 154, 158, 160 
rating of traction, 70, 147 
reversal of, 59, 154, 156, 192, 195 
self-regulation of, 119 
speed regulation of, 131, 151, 165, 168 

compound motor, 135 

series motor, 135, 136 

shunt motor, 135, 137 
speed variation in, 

compound motor, 119, 138 

series motor, 118, 127 

shunt motor, 118, 125 
types of, 118, 119 
Motors, traction, 
Dick-Kerr, data of, 131, 132, 145, 146 
series, 145-162 
shunt, 151, 166 
types employed, 145 



N 

Negative booster, 31 
Non-conductors, 22 
Non-inductive resistance, 7 
North-seeking pole, 1 1 



O 



Ohm, 21 

Ohmmeter, 23 

Ohm's law, 25, 26, 39-42, 65, 66 

Open circuit, 32 



Parallel, 31 
batteries in, 33 
dynamos in, 32, 33, 156, 198 
full, 151, 152, 153, 154, 159, 162, 192, 

195, 197 
motors in, 151, 152, 153, 154, 159, 160, 

195, 197 
notches, 154, 157, 159, 161 
resistances in, 34, 41 
Paralleling, late, 160, 162 

early, 162 
Path of current, 

from generating station, 3 
through car, 5 



Permeability, magnetic, 16 
Polarity, 
dynamo test for, 14 
magnetic, 11 
Poles, 
magnetic, 10, II 
positive and negative, 31 
Potential diflference, 21, 39, 40 

energy, 99, 112, 117, 162, 163, 
171, 172, 201, 205, 206, 207 
recovery of, 117, 162, 172, 206, 207 
Power, 69 

and work performed, 70 
electrical, 70, 72, 76, 82, 83, 84, 86, 117, 
139 
Pressure, electrical, 21 
Principle of distribution, 1 
dynamo, 43 
motor, 56 



Q 



Quantity of electricity, 21, 72 
of heat, 24 



R 



Rails, 

as conductors, 3, 30 
bonding of, 31 
thrust on, 102, 104 
wear of, 104 
Rating of traction motors, 70, 147 
Raworth's regenerative system, 165 
Regeneration, examples on, 117, 200, 206, 

207, 208 
Regenerative braking, 164, 176, 190 

systems, 145, 162, 165, 168 
Residual field, 53, 54, 188, 195, 196, 198 
magnetism, 12, 53, 54, 186, 188, 
196, im 
Resistance, 

and heat, 23, 32, 63, 84, 138, 176, 185, 

186, 189 
and temperature, 26 
incandescent lamp, 39 
internal, 30 
non-inductive, 7 
to flow of electricity, 21 
to traction, 94, 95, 114, 116, 143, 201- 
208 
Resistances in series and parallel, 34, 41, 

42 
Retardation, 89, 113, 175, 203, 204 
Retarding force, 91, 109, 110, 111, 117, 
179, 181, 205, 206 
in electric braking, 117, 176, 180, 181, 

182, 183, 186, 190, 191, 205, 206 
in mechanical braking, 178, 179 



2l6 



INDEX 



Retentivity, magnetic, 12 

Return feeder, 31 

Reversal of motors, 59, 154. 156, 192, 195 

Rheostats, 3, 5, 156, 159, 184 

Right-hand rule, 45 

Romapac tramrail, 104 



S 



Sand, application of, 178, 182, 183, 185, 

187, 189, 191, 193, 197 
Saturation magnetic, 17, 54 130, 137, 148, 

166, 186 
Secondary actions in motor, 141 
Section feeder box, 3 
insulators, 3 
Separate excitation, 51 
Series, 31 

connecting batteries, etc., in, 32, 33 

dynamo, 51, 53, 54 

dynamos in parallel, 156, 198 

full, 151, 152, 153, 154, 157, 158, 159, 
160, 161 

motor, 118, 127, 145-162 

motors in, 151, 152, 153, 154, 158, 160 

notches, 154, 157, 158 

parallel control, 151, 167, 168 

resistances in, 34, 42 
Short circuit, 7, 22, 32 
Shunt, 31 

dynamo, 51, 52, 53 

motor, 118, 125, 151, 166 

regulator, 53, 135, 165 
Skidding, 178, 179, 182, 183, 185, 187, 189, 

191 193 
Slip of wheels, 94, 102,' 193, 196 
Slip rings, 47 
Solenoid, 6, 15 
Speed, 87, 112 

and acceleration, 88, 90, 108-111, 112, 
117, 161, 175, 201, 202, 203 

attained on given gradient, 97,117, 174, 
201, 202, 203 

uniform in traction, 108, 109, 110, 111, 
144, 150, 159, 160, 166 

control, 163, 164, 167, 190 

equivalent values of, 88 

formulse, 106, 107, 174, 175 

power and D.B.P. of series motors, 145- 
162 

power and D.B.P. of shunt motors, 151, 
166 
Speed regulation of motors, 131, 151, 165, 
168 

compound motors, 135 

series motors, 135, 136 

shunt motors, 135, 137 
Speed and wheel revolutions, 105, 107, 114 
Speed variation in, 

compound moture, 119, 138 



Speed variation in — contd., 
series motors, 118, 127 
shunt motors, 118, 125 
Starting a car, 157 
a motor, 62 

resistance, 63, 63, 66, 154 
switch, 63, 154 
Switchboard main, 1 



Tables of traction motor data, 132, 147, 

150, 152 
Temperature rise, 24, 123, 142 

in traction motors, 70, 146 
Terms, 

" dead," 8, 20 

" live," 7, 8, 20 

open circuit, 32 

parallel, 31 

positive and negative poles, 31 

series, 31 

short circuit, 7, 22, 32 

shunt, 31 
Test for direction of current, 14 
Test of series motor, 75 

traction motor, 131, 132, 145, 146 
Time element, 

in braking, 199 

in fuses, etc., 38 
Theory of magnetism, 13 
Torque, 76, 85, 181 

and B.H.P., 79, 85, 106, 114, 123 

and D.B. pull, 102, 106, 114, 117, 205, 206 

and load, 121, 123 

at driving axle, 101, 114, 117, 205 

effective, 79, 121, 124, 141 

measurement of, 79, 80 

of a motor, 78, 103, 124 
Torque of series motor, 79, 129 

shunt motor, 127 
Torques, 

balance of, 76 

balance of, in motor, 121, 133, 135, 136 
Traction, 

balance of forces in, 108, 110, 111, 144, 
159, 160 

consumption of energy in, 82, 84, 163 

D.B. pull required in, 90, 97, 108, 109, 
110, 114, 116, 117, 143, 147, 150, 152 

energy expended in, 09, 162, 171 

H.P. expended in, 98, 106, 107, 108, 114, 
116 

load on motors in, 144 

series motors applied to, 145-162 

shunt motors applied to, 151, 166 

types of motors, 145 
Tractive effort, 94, 95, 100, 102, 104, 143 
Tractive resistance, 94, 95, 114, 116, 143, 
201-208 



INDEX 



217 



Trolley standard, leakage on, 7 
Trolley wire broken, 7 

" dead " and " live," 7, 8, 20 

pressure at, 1 

section, 3 
Trunk leads, 5 



U 



Uniform pressure in dynamo, 49 
Uniform speed with motor, 120 
Uniform speed in traction, 

requisite conditions, 108, 109, 110, 111, 
144, 159, 160 

with series and shunt motors, 150, 166 



Volt, 21 
Voltmeter, 23, 34 



W 



Water a conductor, 22 
Water resistance, 26 
Watt, the, 71 

hour, 72 
Wattmeter, 72 
Watts expended, 

calculation of, 72, 76, 82, 83, 84, 86, 117, 
139 

measurement of, 72 
Windage, 141 
Work, 

and power, 69, 70, 71 

principle of, 67 

rate of doing, 69, 82, 83 
Work expended in, 

accelerating, 98, 99 

mounting gradient, 96, 98, 99 

overcoming friction, 94, 98, 99, 202-208 



THE END 



PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLKS. 



HARPER AND BROTHERS' 

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